Copyright and trademark often doesn't count when the business is completely separate from the existing entity. So if say someone opens up Big Dave's as a Pizzeria in Miami, FL and there's already a landscaping company in Tampa, FL called Big Dave's then they're not likely to get punished under trademark laws or even if there's another Big Dave's Pizzeria in Atlanta, GA. The markets don't overlap. So there isn't any case. However, if there was already a Big Dave's Pizzeria in Miami than that original company could indeed make a Case that the new location stole their name and is unfairly profiting off of that name because of it.

This particular xase may be different however as it's quite possible that they could prove that the flower shop knowingly used the name to profit off of the band's success which is generally why Copyright laws were created to begin with.