Hawks:
Hawks begged and begged you to let him buy a sugar glider also referred to as a flying squirrel after months of bribing you finally gave up and let hawks buy a sugar glider you both agreed on the name sugar because I mean? It just fits and you both love to fly around the house with him
Dabi:
The "thing" as Dabi likes to refer to it just wandered into the base one day and while everyone was fighting over who had to get rid of it to dabi's absolute horror you fell in love with the "thing" and claimed it as your pet eventually Dabi warmed up to "fuzzy"
Monoma:
You'd always loved bunnies and monoma suprised you with one for your birthday you ended up naming him mr.hops monoma loves him but the bunny doesn't seem to like him very much
Bocogo:
You got a pamiranian as a joke to make fun of Bocogo but you both loved the little firecracker and kept him you named him "devil in disguise" but You later found out "devil in disguise" is actually a girl but the name stuck
todoroki:
After taking one look at "princess" you fell in love she reminded you so much of Todoroki and when you found out she'd be put down if no one adopted her with in the next week you immediately adopted her Todoroki was suprised but glad that you saved the cat from being out down
Twice:
Yeah. A fish. I'm tired lemme alone
Kai:
-Kai thinks pet's are discussing and dirty so you don't have one
Shigaraki:
You got a corgi sence Shigaraki used to have one you named him cutie