I'm not certain about the Moments question. However, if Photos doesn't seem to be detecting a face, you can always add it manually.
The way to do it isn't difficult, but I admit that I struggled to remember how to do it as I wanted to give directions. Ensure that your Info pane is open (command+I to open it via keyboard shortcut), then open the photo. Starting from the top, you should see the EXIF pane, "add a description," "add a keyword," and then "Add Faces" with a big + button. Clicking that will bring up a little ring that you can move and resize to fit the face, and you can then label who it is.
I don't know that it forces face detection, but another useful (and more automated) function is the face review feature. If you select the People area from the left-most column you should see a bunch of people you've tagged before, with those you have favorited on top. Double-clicking on someone will bring up all of the photos that they have been tagged in. If you haven't done this in a while and had a bunch of new photos, Photos may prompt you to go through some additional photos to confirm or deny that the person is in them. Otherwise, scroll all the way down to the bottom and click on "confirm additional photos." Photos will show some activity about searching for additional photos, and it then presents you with one photo at a time for you to indicate whether it's right or not. If you indicate that it's correct, it will usually automatically add a lot more than just the one photo that it showed you. It's fun and pretty neat, but with macOS Catalina I find that Photos performance has really bogged down in general, and unfortunately the face review has suffered horribly in the speed department - and I've had the program crash on me a few times while going through it. Hopefully it will be fixed in the coming versions.