You can choose whichever name you feel fits you as long as you don't break any rules like Be nice.
As far as I know nobody encourages people to use their real name and nobody encourages people to use an imaginary username. That's about it. There are no rules and no encouragement for either side.
You should just do what you feel is right for you. If you don't have a problem with using your real name then that's fine. If, on the other hand, you feel better with an imaginary name, then by all means - use that one.
I, for example, prefer some measure of anonimity and chose not to use my real name. So far nobody has complained.
But there are a lot of people who (at least seem to) use their real names. Sometimes the first name, sometimes the last name, sometimes both, sometimes abbreviations, ...
Choose whatever you feel comfortable with.
Anonymity certainly is useful in encouraging fair and open discussion, but it may also make it easier to attack a person individually.
What we want is to have fair and open discussions. If someone resorts to individual attacks we politely refer that person to Be nice. and flag the message for moderator attention. Be nice. That's the only real rule about behaviour in discussions on the site and that one is not only encouraged, it is enforced by the whole community and in special occasions by moderators.
If someone fails to be nice because they think they are anonymous - we don't really want that sort of people here. Your username should therefore not make any difference and I don't see any reason why we should resort to encouraging people to use their real names. It might deter some people who we want on the site and everyone who fails to be nice because this is the internet should search for a forum where they can use their anonymity to attack individuals. That sort of behaviour won't be tolerated here.
In conclusion: No, we don't care whether users use real names or not.