All the World's a Stage
No one can tell you exactly how to roleplay anything, so take below as a helping hand and a guide - not a rulebook.
With the announcement of World of Warcraft: Cataclysm, the Worgen became quite popular. While they are based on werewolves they also subvert many werewolf archetypes; they can change forms at will, and do not lose control in their more bestial form. This contrary nature, along with the mysterious history of the kingdom of Gilneas, makes for some interesting roleplaying.
"Damn the orcs, damn the Alliance, and damn you! The last thing Gilneas needs is sponges from other nations drawing from our resources, Dalaran wizards meddling with our affairs, and someone else's enemies killing our soldiers! Gilneas is its own nation and it always will be." - Genn Greymane, on foreign relations.
All playable worgen are citizens of Gilneas, an isolationist kingdom, reluctant to assist other nations in times of war, going so far as to completely withdraw from the rest of Azeroth with the construction of Greymane Wall roughly twenty years ago. Gilneans did not participate in the Third War, even refusing to allow Lordearonian refugees of the Scourge invasion to enter the kingdom. During the events of World of Warcraft: Cataclysm, the city of Gilneas is attacked by a group of Worgen, the products of a curse created and spread by the Archmage Arugal in the nearby Silverpine Forest. These attackers spread the curse to those of the city's population that survived being attacked by the invading Worgen. Those who were affected became viscious worgen, unable to stop themselves from killing their former friends, neighbours, and family. After a civil war of sorts between the cursed and un-cursed Gilneans, the human side developed a serum which gave the curse's victims some control over their transformation. You will start as a Gilnean citizen who has assisted with the defense of Gilneas against the invading Worgen, only to be bitten and cursed yourself. Eventually you become a cursed worgen who has recently been captured and injected with a double-dose of this serum. While you are still working to cure others and fighting off an attack from the Forsaken, the cataclysm occurs, reducing the Greymane Wall to ruins and bringing an end to your kingdom's isolation. Eventually you come across a group of Night Elf Druids of the Scythe. After a conversation with them, you come to discover that the Worgen Curse originated from them when they attempted to take the form of their patron, Goldrinn. In doing so, they lost themselves to the ferocity and animosity of their new forms, turning them into mindless humanoid wolves. Their fellow druids who remained unaffected put them into a magical sleep beneath the tree of Tal'doren. There they slept until discovered by Arugal. He sought to use their magical state for his experiments, and in doing so, created the Worgen Curse. After learning this story, you work with the Druids of the Scythe to preform a ritual to prevent you from devolving into a mindless beast, as the medication you have been given will only last so long.
How does the history of Gilneas affect you? Remember, Gilneas and its people have had almost no contact with the outside world for about twenty years. (Keep this in mind when deciding your age.) The years of isolation have likely shaped your history and personality more than anything, aside from your curse. If you are young, you would have have never ventured outside of Gilneas, or at least have no memories of doing so. If you are older, you may have participated in the Second War. Regardless of your age, recent events such as the discovery of Kalimdor, the specifics of the Third War, the arrival of the draenei, the defection of the blood elves to the Horde, the reopening of the Dark Portal, and rise and fall of the Lich King, may be completely unknown to you or only rumors. (Lore connections to the Third War are so ubiquitous in WoW, it may be a good idea to read up on it just to remind yourself what your character wasn't connected to and wouldn't know about.)
You are a citizen of the human kingdom of Giles first and a worgen second. Your curse is a recent one, so regardless of age you've spent most of your life as a human. Remember these facts when choosing your name. So far, the NPC names we've seen in the worgen starting zone have been human sounding, indicating the most Gilneans have not used their recent curse as an excuse to change their name to Bloodpelt, Gorefang, or Feralclaw. However, it is not yet clear which NPCs have been affected by the curse and which have not. (the obvious exception being the Gilnean king, Genn Greymane and his ilk)
If you are going the split personality route, and your personalities have two separate names, then you will need to decide which one is your screen name. This decision should flow from how you are going to introduce yourself to strangers. Do you carry a shameful curse, or are you proud of your new abilities? Are your feral aspects dominant, or are they kept in check? Using Blizzard's paid character re-customization service, you could even start with one name, and switch to another as you develop.
For your surname, you could take a cue from Genn Greymane, and simply have gotten lucky, having already had a feral sounding last name (Barker, Wolff, et cetera). There is a strong precedent for such occurrences in fiction (Captain Hook, Otto Octavius), but it may come off as slightly cheesy. If you are more of a strict lore-follower, you may want to borrow your surname from a Gilnean NPC since it is likely a relatively small kingdom like Gilneas has a relatively small number of families. As Gilnean dress and architecture seems to be inspired by Victorian era England, you could also take your first and/or last name from a list of British names. There are also a good deal of Gilnean names that are not strictly English, but ones like 'Archibald' and 'Sean' that are Welsh or Irish. These are also acceptable.
You could, of course, always adopt yourself a title, changing your last name. Your name only has as much meaning to it as you give it, and as such, your name is whatever you identify yourself as. Perhaps you have found your "curse" to be a boon, and are proud of your new found abilities, and you wish to leave your old, "worthless and weak" identity behind you. You could then choose a surname reflecting your achievements, or personality, much in the manner of Gnomes. Just be sure to make it known when necessary.
"Pah, the fountains in Gilneas could grant ten times as many wishes as Dalaran's!"-Genn's Copper Coin
Creating a personality for your worgen isn't much different than creating that of a human or any other race. There are however, three key ways you are different from other races; your strong sense of nationalism, your humiliation by recent events, and your worgen curse. Try starting with the alignment and personality of your choice, and then adding these three traits on top of that. You might get something interesting.
Integrating Nationalism into your personality is the easiest of the three. You love your country, and you think it's the best. The above quote is a perfect example. You believe that Gilnean people are the best, the Gilnean army is the most powerful, your king is the best leader ever, Gilnean food tastes the best, the culture is the most advanced, etc.
How nationalistic your are has probably been determined by your age more than anything. If you are young, you would have grown up behind the Greymane Wall, surrounded and raised by people with a very high opinion of Gilneas, without any exposure to other cultures and ideas. If this is the case, imagine what it would be like to venture out in the world for the first time and learn the most outsiders don't think so highly of your king and your people. How would hearing a contrary opinion for the first time in your life affect you? Older characters may be more traveled, giving them a greater sense of Gilneas's place in the world, or what they've seen may have only further convinced them of Gilnean superiority.
Once you've decided just how nationalistic you are and why, you need to think of creative ways for that nationalism to manifest in your RP. You could like to brag about how super-awesome Gilneas is, or be prone to getting into duels while defending your kingdom's honor, or you may keep your opinions to yourself while a festering hatred for all other nations slowly builds inside you. However you decide to (or not to) express your nationalism, as with all actions in RP, it should always flow from your personality and history.
Within a (somewhat nebulous) short period of time, your kingdom has been cursed, ravaged by civil war, had its precious wall broken by an evil molten dragon's return from another dimension, and been attacked by the Forsaken. As if that wasn't bad enough, these events have forced Gilneas to come crawling back to the same Alliance it reluctantly joined during the Second War and gave a big middle finger to during the Third.
How much these events have tempered your pride and nationalism depends on your personality before they occurred. Regardless of where you start and where you end up, these major blows to your culture, along with being cursed, should have some effect on you. This change may have already happened, or it may be an ongoing part of your development as you slowly come to grips with what has happened.
It may be the case that the worgen curse hasn't affected your personality at all. Now you are a human, with all your memories and cognitive functions intact, who has merely gained the ability to transform into a feral-looking form. Sound boring? Well, a worgen with complete control is not necessarily without inner conflict. You may see this curse as a blemish on the good name of Gilneas, or perhaps you are vain and disgusted with your own appearance. You may also become more feral simply because you believe you are an animal. Take the prince in Disney's “The Beauty and the Beast,” for example. It is never stated that the enchantment affected his personality, but for psychological reasons he still became bestial in nature; growling, walking on all fours, and being generally anti-social. By the end of the movie, he's essentially acting human again, even before his magical tear-jerking transformation. Perhaps your human mind and Gilnean pride has seen your new status as a gift, a means to defend Gilneas, or bring others to see how great (you think) it is. Your new strength and agility have given your courage and bolstered you (well earned or otherwise) pride in yourself. You retain a human mind and yet embrace your new body.
Two Minds Edit
Another way to roleplay a Gilnean worgen that is popular with some roleplayers is the idea of two conflicting (or coexisting) minds within your character. The first is your character's original human personality and the second is the worgen personality introduced into your mind by the curse. You may be strictly human when you are human and worgen when you are worgen (ala Dr. Jekyll and Mr. Hyde) or that line may be more fuzzy, with your form merely dictating which personality is dominant at the time. You may be normal as a human, yet fighting the usual aggressive nature of the worgen while in feral form. Needless to say, this method is not for everyone, and should be used with caution. It can be a bit difficult to pull off correctly. Or, if you prefer the comedic route, you can treat each form as a separate person and argue with yourself.
Feral Instincts Edit
The middle ground in worgen RP is the "feral instincts" approach. As with “complete control,” you have a single personality, but the curse has made that personality more feral. Your level of “ferality” while in your two different forms may be the same or it may be very different. If you're willing to bend the lore a bit, you could even be more civilized in your worgen form! (Though you better have a damn good explanation as to why that is.)
The only origin exception you have is if you chose to be a Death Knight. As a Worgen Death Knight, you are a former slave of Arugal. Instead of talking over how you feel about the curse, you should instead talk about your 'freedom' or treatment by Arugal.
This part looks simple, you are a normal human, or you may choose to stay in worgen form. Either way, remember that Gilneans care about what they look like. They are aristocratic in appearance, wearing clothing typical of the Victorian Era. Even if you're more of a blue-collar type, just remember to always look good. After all, you're a Gilnean, you're way better than everyone, right? And you need to be dressed and ready to climb that social ladder among your own people, to become the "elite of the elite" so to speak.
To know a little more about worgen and the history of Gilneas, see the following links: