We had this same problem in a band I was in.....fighting over a name.
I wanted our name to be The Rolling Stones.
It seems that there’s another band with that name.
So we called ourselves Herb Alpert And The Tijuana Brass.
Mel Blanc once had a band called the Tijuana Strings.
https://www.youtube.com/watch?v=vvrPnsgmNbQ