Most probably nothing. But I’d change the name if it was his sole creation, cause it’s probably good karma. Plus, he will probably be a pain in the _ until you change it. And you don’t really want to continue the legacy of an ex band member anyhow.
If he didn’t make up the name completely himself, and you all contributed, he can sod off and has no legal or moral recourse.
Could you switch back to the old name before the fired member? How established as a band are you with the existing name?
Also, could you change the band name to Batscquatch?
Or change to Switchback, as a tribute to your Douchy ex band member. But then I want compensation for the idea. I accept payment in the form of high fives, kudos, and on special occasions freshly baked pastries. (Not those kind

)