Sure, some may use nicknames or professional names because they're more marketable. But others use pseudonyms for privacy protection. They want to compartmentalize their own identity, and I consider that a perfectly valid purpose.
So during day to day business and life, you can call yourself whatever you want. Others can insist on identification if it's important to them, and that gets trickier.. but using a pen-name on a book or a hotel reservation is no different than using a fake name at starbucks while waiting for your coffee.
Forging documents is of course illegal, so that puts a crimp on things - but there is no particular reason that you are required to use your "real" name except when dealing with government documents (and things that rely on them)
The technically safest advice is "don't talk to the police": http://www.youtube.com/watch?v=6wXkI4t7nuc
Allow that to empower you and the truth will literally set you free. Truthfully, you are almost always free to lie. Find those boundaries and tiptoe without crossing them.
I imagine that even if you are able to take advantage of some of the other advice in this thread about gaining actual documents and whatnot, you are more likely to get caught if you aren't willing to stretch the truth or lie.
"Out on the edge you see all kinds of things you can't see from the center."
I really enjoy watching fox news or listening to rush limbaugh and I find that the longer I take it in, the more I learn how to hone this practical skill.