Adding a new named person to a photo not working

Well, we can maybe narrow down the problem-- try these things:

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

           Start up your Mac in safe mode - Apple Support 

Those are the easiest things to try first. Then try these:

• 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.
• Make a new user and see if the same problem recurs with it
• Rebuild your Photos Library--close Photos and re-launch by option-command-clicking the app icon.

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.

Let us know what happens…

You're right, sometimes the circle refuses to move. This is because Photos thinks you're still in the info window and you want to drag the picture to there, or something like that. In that case you need to tap on the picture to let Photos know you mean the picture, and then you can move the circle. Or, you can just type the name first, and then move the circle.