Some pets I can merge - others I can't - WHY?

I've had this happen when one set was identified as a person rather than as a pet-- maybe left over from before you could do pets. You can't merge people and pets, apparently. I was going to say that I can't remember what I did to fix it, but

apparently I never did fix it. If you have any ideas, I'm listening…

OK-- I've been playing with Chessie. I clicked on her and said "This is not Chessie." It offered for me to tell who it really was, and it apparently decided this was a pet, so I scrolled through the pet names for Chessie. She's in the right spot now-- there is only one Chessie!

One thing is that you might need to allow some time to elapse between changes.

Photos scans the pictures and records the attributes of faces it finds. Then, when you name a bunch of faces as the same pet/person, it learns which attributes go together. So when you make a change, you may have to wait for it to forget what it previously thought were Nigel#1's characteristics and not Nigel#2's characteristics. One way to do that is to say that none of them are Nigel, and to name all the Nigels as RealNigel or something. Then they'll all go in the same bin, and Photos will have a chance to forget what makes up Nigel. Give it some time, and then you can change RealNigel back to Nigel.

I can't remember what names go with what faces, either…

The "people&Pets" allow us to have two People or Pets with exactly the same name, because we may different people with the same name. That is the intended behavior.

Which system version do you have installed? Some older versions of macOS did not not allow us to make two faces in the same photo as the same person. when we tried, it would create a second person. For example, in a photo of a person standing in front of a mirror we could not mark a person and the mirror image with the same name. Or , when Photos had already assigned the name of some person to a face in the image, but did not yet show the name and has been waiting for a confirmation, we could not name a different face with this name, if Photos had made a mistake.

Have you tried to drag the cat named Monster onto the duplicate? That should merge them, if possible. Or click into the name field of the duplicate and name it to the the name of the first cat.