No u don’t need to include but if you are running ads for business which is geo target then having the city name will help boost CTR.

Example .. xyz service southern california had a lot of character but using it as local lingo i.e. xyz service SoCal

Xyz service north boulder has a lot of character but using it as local lingo i.e. xyz service NOBO

This strategy will help boost business reputation because it’s such a local lingo and only locals use