It's kind of a problem. I knew a Chinese girl who chose the English name "Squirrel." When I told her it wasn't a real name, she didn't quite understand.
Yep - Douglas Squirrel (http://douglassquirrel.com/) is a guy in London who does a lot of work with startups, and he is mostly known just as 'Squirrel'. Really cool guy, by the way, if you get the chance to talk to him at a meetup.
Well, my SO calls me that as a nickname. I have ginger hair and I am kind of impulsive. That and a squirrel came eating out of my hand one of the first times we met.
What's "not a real name?" A name just something you are known as so there's no 'fake' names by definition. Some of my family have totally nonsensical names. I don't tell them they have fake names. Squirrel is pretty 'normal,' people have been taking animal names forever.