Hello rwzpv,
Welcome to Apple Support Communities!
We see you viewed the Apple Support page for Get help with the Photos app on your Mac - Apple Support
It sounds like you're using these steps to identify people in a photo:
"Manually identify and name people in a photo
Some photos may contain people who are not automatically named. You can name them manually.
- In the Photos app on your Mac, double-click a photo to open it.
- Do one of the following:
- Choose View > Show Face Names. Click the name (or click “unnamed”) under a face, type a name, then press Return (or choose a name that appears as you type).
- Click the Info button in the toolbar. Click the Add button, drag the circle to position it over the face if necessary, click the Name field, type a name, then press Return.
- You can click the Add button multiple times to identify multiple faces in a photo. To remove a name that you added to a face, click the Remove button on the person."
This Apple Support page has the full details: Find and identify photos of people using Photos on Mac - Apple Support
Does the issue persist after a normal restart of your Mac? Are you able to test in a test user account to see if it's a software related issue?
We hope this helps.
Cheers!