Merging two people in Apple Photos while preserving individual tags

Use a Smart Album like this:

You go to the menu File>New Smart Album.

If you're new to Smart Albums, it's pretty straight forward as you see above. Also, you can see this:

Create Smart Albums to group photos and videos automatically on Mac - Apple Support

Most of us also include the person's name in the Keyword section, so it's easy to include people with their faces turned, for instance. Normally, I'd be more likely to use a Smart Album with Keyword is Ann, and so on. You start by going to the Ann person album, selecting all, and add Ann as a Keyword to all at once. Keywords don't show up in iPhones, but searches work for them, anyway.

Do not merge two separate people. That will interfere with the face recognition and Photos will no longer be able to recognize the faces of the merged people.

If you want to find the photos showing two certain people, for example the photos showing your parents together, define a new group in the People&Pets album, showing your Mom and Dad together. See: Find group photos and videos on Mac - Apple Support (EG)

Create a group

You can create a group with any combination of people and pets from the People & Pets collection.

1. Go to the Photos app  on your Mac.
2. Click People & Pets (or People) in the sidebar.
3. Click Create (to the right of Groups), then select people or pets to include in the group.
4. Click Add.