You don't say what iOS you have. Updating can cause a re-scan of faces, so if you don't have iOS18, you should try updating.
On an iPhone or iPad, you can't directly name a face that Photos doesn't recognize. One "workaround" would be to do it on a Mac, which allows you to select people and name them, even if the face isn't recognized. It's what I do, but I'm guessing you don't have a Mac, so this won't work for you.
Another thing that I do is include the name in the Caption field in the Info window. Then, if you search for, say "Caitlin Clark," you'll get the ones that Photos recognized and also the pictures with "Caitlin Clark" in the caption. To be able to search this way, the name needs to be first in the caption.
This is good practice in any case. Face tags can be lost in OS update, and they don't transfer with an exported image file. But captions export with the picture. I include the name in the caption for every picture that has a recognized face, as well as for un-recognized faces.