Quote:
“One of my cats.” If need be, e.g., “the younger one.”
Going to lengths to describe the pet every time instead of just saying the name seems just as weird as saying "my second youngest brother" to me.
Again, given that the person you're talking to know the name of the person/cat/dog/whatever that is being referred to, I don't see why you shouldn't use it. That's part of what names are for after all.