Actually your missing the whole point. It was joked about in the book and the pilot episode, when he told her his name and she started cracking up at how mundane it was. Also, the fact that the town knows him as "vampire Bill" is also quite comical out of context.
You also have to remember Bill is about the least flashy vampire as vampires come; he's quiet, old fashioned, and basically a normal undead-guy. His name is used to reflect this image.
his actual name is William and bill is short for that. It works because they live in the south and so it might seem silly but it does work pretty well.
