I think it's because that's the name of one of the servants in the Fate series.
See, the idea I had is that Joker would use 5 Personas (which is probably a little much): Arsene (his starter/main one), Jack Frost (the mascot), Pyro Jack (the other mascot), Pixie (usually the first demon/persona you get), and Alice (because why not)
Oh. Yeah, actually, it could very easily be that he's famous from Fate and therefore people like to see him in other things...
Also, I like your selection of 5. All top-notch choices.
If Joker really DOES get 8 Personas (likely to represent each element), who would they be if they aren't his friends' Personas?
We have obviously Arsene for Eiha spells
Jack Frost is the most likely candidate for Bufu spells
But what about Agi, Zio, Garu, Frei, Psio, and Kouha?
Well, that'd be an insane number of Persona. Sounds fun!
Eiha: Arsene
Bufu: Jack Frost
Agi: Cerberus (one of the most reoccuring MegaTen demons and one of the OGs from the novel)
Zio: Thor (reoccuring and important, plus generally famous on his own)
Garu: Matador (fairly common demon, generally unique design-wise and from a less-commonly-covered folklore)
Frei: Suzaku (appears semi-regularly)
Psio: Shiki-Ouji (fairly common demon, super-cool-looking deisgn)
Kouha: Anubis (reoccuring enough demon, plus generally known figure)
Bonus, if we're being insane, then let's go all the way...
Phys: Cu Chulainn (third most popular demon, from a unique mythos)
Almighty: Alice (second most popular demon, one of the most reoccuring demons)
Dia: Pixie (generally a secondary MegaTen mascot, given her playable status in Jack Bros and in Puzzles + Dragons' P5 crossover)
I think this list covers a variety of mythologies without including anything likely to offend someone (i.e., avoiding Abrahamic religions, as I imagine there would be some bad press if Nintendo let you summon satan in their party game).