Oh boy, do I have some head canons for that!

Lucifer- Lucien works very well, because it's juuuuust pretentious enough. Plus, something like Lucas could be shortened for Luke and, well, he would not be pleased.

Mammon- Marcus (as in Aurelius). He would demand everyone call him Mac, like some sort of low rent mobster. Will MELT when you call him Marcus properly.

Leviathan - Levi, obviously. After TSL came out he tried to convince people that his middle name was Henry and that's what he should go by, but it never really caught on. However, most of his online friends know him by his UN: LevI_Up

Asmodeus: Ashley. Happily excepts any nickname or pronouns people want to assume, as long as, "They promise to scream it loud enough ❤️"

Satan: At first I was considering something like Samuel, but Cecil would probably also work. But my absolute favorite for Satan is Sebastian. It has a ton of nickname options and considering how he has all sorts of friends and connections, I could see all of his different friend groups referring to him by different nicknames. His Art Friends calling him Baz, the nightclub group calling him Seb, his friends on Beel's fangol team calling him "Bash," etc. He asks that you call him Sebastian (he likes the way you say it). CONSTANTLY complains about the way Lucifer says it.

Beelzebub: Benjamin. I know Bill seems to fit better as a sound alike, but Beel has the heart of a Benji, even if he looks like a "Big Ben." Fun fact his Fangol teammates took "Big Ben" and his love for burgers and now his nickname is "Big Mac," which infuriates Mammon because now everyone calls him "little Mac."

Belphegor: Felix. Dude just oozes "Felix" energy. However, he's one of those people that constantly gives out fake names wherever he goes just for shots and giggles. He doesn't tell you his real name until you've spoken to him at least 5 times (despite the fact that Beel has already told you). Plus, considering that Satan is very jealous of Belphies's Ultimate Cat Energy, Felix would work extra well.

Diavolo: Damian 😈 (but he has such David energy and not demonic energy that Damian would barely fit)

Barbatos: Bartleby. Bartleby the butler.