I don't know why the character name was changed in the TV series but in the original comic stories, Banner's name was (Robert) Bruce Banner so the film uses the original name.
He was originally Dr Bruce Banner in the Marvel comics but in the late 70's when the show was adapted for TV the name Bruce was considered to be too stereotypically gay at the time and was changed to David. They left Bruce in as his middle name.
As a tribute to the original comic, Banner's name is seen as "David Bruce Banner" on a gravestone in an early episode (maybe if memory serves the end of the pilot).