SEA1K4EVR is right. 1st, it isn't the FAA, but the TSA, and 2nd, it is name as it appears on govt issued ID that will be used for travel. If your travel will require use of a passport, than use the name on the passport. If flying domesticly, and you wish to use a DL instead of a passport, make it be that name.
Here is a link for you:
http://www.tsa.gov/what_we_do/layers/secureflight/