I JFGI and the majority of images of 78 labels say "his" rather than "the".
This
isn't surprising - not to me, anyway. When I was a kid, big bands were
still a "thing". Notable bandleaders would often gather their band
together themselves, so the band would often (but not always) be named
something possessive - as in "Guy Lombardo and His Royal Canadians".
It's
difficult to change these things when the evidence stares me in the
face AND I can actually remember how these things were done back then.