That's a good question. I've heard of dozens of specialized words for the collectors of this, that, and the other thing, but there may be no word for a hat collector. There's even a word for people who collect beer mats (coasters) -- that's a tegestologist -- but I don't know the word for hat collector. Of course, a milliner is a hat maker/seller, but that's not what you're looking for, I'm sure.
This may be your opportunity to coin a new word!
As nobody has claimed this title, I hereby declare that the new name for a collector of hats is a "Nowakologist"
As far as I can see, I just make note of the time and date, and observe than nobody has attempted before
tin collector
The correct name for the graduation hat is a mortarboard.
It is obvious! the name is a thing you call shoe collector!
No
A stamp collector is termed a - Philatelist
The name of a traditional magician's hat is a top hat. This is the hat that magician's use to pull rabbits, birds and scarves out of.
there is no scientific name for it .it is just a badge collector.
debt collector
A magic hat
top hat
The sorting hat