headcanon about this version of Moon:

[moonsmile]

 
Her smile's not always genuine. It's more of a disguise--to hide how shy she felt when she first moved to Alola, to hide how nervous she was when she got her Litten, to hide how bemused she was at Aether, and even to hide how charming she found Team Skull.

Not that she didn't think they were ridiculous. They were. But she liked their ridiculousness right off, and their style.

She knows the smile's unsettling, and she doesn't mind that. She even purposely made herself more creepy for a while--yellow contacts, stringy hair, mostly-black clothes (with some white accents for a tiny bit of Team Skull reference, but it was mostly due to her upbringing in Kanto. White symbolizes death there). 

Moon mostly dropped all that after the Mother Beast incident. At least the contacts. Sometimes she gets back to her gothpunk getup and hair and puts flowers in place of her hat when she feels like changing it up.

Her team consists of 'creepy' or 'mean' pokémon as well--she always has Incineroar, Midnight Lycanroc, and Mimikyu with her. Lunala is always at her side, though they can seem 'creepy' as well. 

Nebby was nicknamed Nebbie, since it's a closer spelling to 'Lillie' and it made her feel better about travelling with them. It's not like anybody else can notice a difference.

She caught all of the (Moon version) Ultra Beats. They're hanging out on Poké Pelago.

While she hunted down and fought them all, none of the Tapu were caught, just defeated. It didn't feel right taking them from their islands, and she was pretty sure none of them wanted to go anyway.

Her own fake expressions, being raised with a Meowth and raising Litten herself helped to teach her how to notice the subtleties of other people.

Yes, she did pick Litten because she was reminded of that Meowth.

She teased Lillie a bit at the start of her journey, though broke off of that post-Trainer School. Moon liked her scandalized reactions, but felt bad after the fact.