I have this same problem (which has persisted over all versions of MacOS), no library repair prevents it happening again. This is a ‘quirk’ Apple has not fixed, it tends to only impact the photos you manually tag (rather than the ones the system identifies for you). Sometimes the tags drop off within a few minutes, days or weeks - there is no identifiable pattern.
To answer your question about names / tags; you can tag using your contacts names or by manually adding a name. The problem with tags dropping off happens to me with both tags linked to contacts and names I’ve added just to the library (when these are manually tagged).
You may like to add keywords to these photos which will allow you to find them again e.g. tag the face and add a keyword to the photo with that persons name. So when you search on that keyword it should do the same thing as opening the people / face album. To help you get a head start, go to the people / face album, select all and add the keyword in bulk to existing tagged faces, then add the keyword to all future photos you add with the same face. Do this for each person you are tagging with their own unique keyword. It’s frustrating but really the only way I’ve found to ‘defeat’ the lost face tags.