Who did the work? If the band parents did all of the work (i.e. room set-up, equipment, open and secure the rooms, etc.), then it would make sense for the money to be a donation to the booster club.
If it’s one director, or the team of directors, then the check goes to them.

That said, I’ve hosted auditions and concerts, organized for the clinician, and have been a Region Band Chair and the checks have always been made out to me. If the other directors from my school helped, I would split the check with them.

Who is doing the work?

Host director gets the check, I take the staff out for a nice dinner with ours.

Depends on the kind of event. We have in some of the handbooks of events that the fee is to the event host (person). That is there because of the prep work that they manage to get ready for the event. At least in all the cases I deal with they're not getting rich off it.

A facility payment would need to go to someone else, but it if it says 'host' that's that person.

It's been a few years, but I recall receiving a small personal honorarium for my time and a larger check to the boosters for expenses.