So far my first motorized bicycle I named "The Atomic BB". I like that name, and have never considered anything else.
My second motorized bicycle was a Cadillac, so it was just named it "The Cadillac". It lived up to it's name too. I've had 2 Cadillac cars, and they were both the worst cars I've ever owned. Always in the shop. The motorized bicycle was just as bad. The motor blew up after 600 miles. After I rebuilt it, it only lasted another 500 miles before it crapped out again. I finally decomissioned it, and turned it back into a riding bicycle, which it seems to like being a lot better.
Now I'm fixing to build a Felt Deep Six. I've kept it in my living room all summer, and have been trying to think of a good name for it besides just calling it "The Felt", but nothing has come to me. I hope I can think of something good. Any ideas?