Photos creates albums of people and pets found in your library when you are not using the app?

broox wrote:. ...

1 My main question is, for this process to complete, should the Mac OS Photos app be open, but not actively being used (i.e. running in the background)? or should the Photos app be completely closed?

2. If I have the "Optimize Mac Storage" option checked, full-resolution photos are moved to the cloud when I'm running low on local disk space. If I'm importing photos, whose full-resolution versions are off-loaded to the cloud before the faces can be tagged, would this cause facial recognition to get stuck?

1. I don't think it matters if Photos is open, but we usually suggest to have Photos open and running in the background. The idea is that if Photos is in the foreground, then Photos figures you're using it and won't let scanning stuff interfere with your work.
2. Optimize Storage has no effect on face recognition.

Adding names is done in the Info window (⌘-i) for a picture. The circle with the plus sign

is for adding a name.

A circle will appear in the picture

and you can drag it over the face. Sometimes you may have to give an extra click in the center of the circle to let Photos know you've changed your focus to the circle.

This works for the times when a face is maybe turned or small or blurred so that it can't be recognized as a face by Photos. You can then type in a name like Prince of Wales, or King Charles III. I've never quite figured out what to do when a person's name changes-- maybe use "King Charles III (formerly Prince of Wales)" or something like that?

Manual face naming is only available on the Mac, not in iOS, so people albums can't be created by us on an iPhone.

broox wrote: ... Look for this process and consider a reboot.

Generally, if you're having unexplained troubles, you do these things, more or less in order:

• Restart the computer (of course)
• Re-start in Safe Mode. This bypasses certain potentially disruptive processes. Safe Mode is different for different computers, so see this: 

           Start up your Mac in safe mode - Apple Support 

• Make a new user and see if the same problem recurs with it
• Use another library if you have one, or make a small test Library with a few pictures in it and see if the same thing happens. You can create a new Library by closing Photos and then option-clicking on the Photos icon.
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.

Obviously the last two apply specifically to Photos. The idea is to find out if the problem is with the Library, with your account, or with caches and login items, and stuff like that. One of these steps may fix the problem, but their failure to work also helps figure out what's happening.