Wallflowers

"Fiercely independent, Jakob Dylan determined early on to make his own name rather than ride on his famous father's coattails. The young musician named his band the Wallflowers after an intense brainstorming session with other band members - and only later discovered (much to his chagrin) that his father had once written a song (albeit still unpublished) with the very same name.

A rider in Jakob's contracts later stipulated that no references be made to "Bob Dylan's son" in any preshow advertising. Ironically, the rider was actually requested by Bob Dylan."

(from anecdotage.com)