Befriending Dogs/Cats and they join your house

Simple as the title really.. Dogs/Cats can befriend you once you pet them enough,and they eventually can join where you live, or maybe enter/leave at will.

Make sure they remember the player who pet them before.

Maybe even name them once u pet them enough times?

Just seemed a cool idea for me.

An older gentleman has a similar idea when you talk to him twice, at the beginning of the game…

In a way, he does fulfill his ambition.