This band took its name from a 1932 movie starring Bela Lugosi.
This band once changed their name to something extremely strange at every show, then were accidentally introduced at their largest show yet as the title of one of their songs and subsequently got good press coverage, causing the name to stick.
In the Tintin books there is a pair of detectives, sometimes called The Thompson Twins. Except that they aren’t actually twins at all. The joke is that all Englishmen look and act the same. Their names are slightly different, (one has a p in the middle). And their appearance is slightly different, there’s a subtle difference in their moustaches.
The Blues Brothers, though, actually ARE brothers in the movie. In the movie they are called The Blues Brothers because 1) they are brothers and 2) their surname is Blues. And when the actors performed concerts as “the Blues Brothers” you could say that they are named after a pair of fictional brothers, but the part “who aren’t really brothers” wouldn’t apply.