Actually it's Ulysses. Phil's mom, being a school teacher, named him after Homer's Greek mythology character, which she was fond of.
With the initials PUF, young Phillip was referred to by his friends as "Puff" (Winchester Tenn. High Yearbook 1968 referred to him as "Puff the Magic Dragon").
This was all well and good until Fulmer brought his career to the less literate confines of East Tennessee, where sportswriters and fans spelled his name phonetically as "Fillup", thus his initials became FUF. His agent, Jimmy Sexton, suggested he drop his middle name a few years ago when they started seeing his name come up on placards and in the media as "FU Fulmer".
Now you know the rest of the story.