if the band has a copyright on their name, like Pink Floyd, Genesis. these are actual legal entity. in other word, like a person. you must get the MP or perharps PR.
in case one of the band members quits on the band .
in music busines history, it is not unusual to have members sue each other for using the band's name. eg. Roger Waters vs Pink Floyd.
I would say this is a matter for someone who is qualified in Entertainment business.
The musicians union in your local would better advise you about this, or if they don't know, they can refer you to an Entertainment lawyer.
p.s.
who owns the band's name? not always the one who formed the band.
again, to quote Roger Waters and Pink Floyd.