A friend of mine always went by a different name than what was on his birth certificate. It wasn't quite the same case as he knew that he was using a nick name. It finally came to a head when the TSA started being a bit more aggressive about checking identities. He did the name change.
If you are an adult, not in the subject of some legal proceeding (civil or criminal), name changes are pretty perfunctory.
One thing I normally recommend (though it may not really be necessary in the poster's case), is to go the clerk after your order is issued and get a bunch of certified true copies of it so you can send them to the DMV, SSA, banks, etc... It's easier if you just blow the $10 while you're there than having to run back and dig up the order later.

