My mayor's name is Soleil, so the nickname I've suggested for villagers to call me is Leila. I think it's super cute!!
I'm still thinking of nicknames for my other three player characters, and I'm thinking of Rion for Orion, Nyssie for Nyssa, and I have no clue what nickname to give Atlas... I'll probably go with whatever villager suggested nickname feels right for him.
Currently all of my villagers are calling me "Fancy-A" which I think sounds kinda silly but hey, I'll roll with it as I didn't want to upset the villager who thought it up. I think one or two of them still call me A-Star though, I admit I like it a bit better but what can you do ?\_(ツ)_/?
I made most of my villagers call me Mayor since I don't like some of their suggestions. However, there are a few that I let call me "june bug" or "Lil' N", because honestly those nicknames are too cute.