How would you name a male pet, Monkey? Since 'scimmia' is female it doesn't seem right. Scimmio, or is that slang for something else?
Maybe call it scimmiotto. The suffix -otto sounds cute in Italian, so it fits to a pet, regardless of age or size.
"Scimmia" is for both genders.
In Italian there are many animals with female name for both genders, for instance: zebra, vipera, marmotta, balena, ...
It's neither English or Italian.
Has connotations of monkey, small and cute.
The masculine suffix suits a male pet.
Can be abbreviated to ketto.