If Photos on an iPhone doesn't find the sort of details to make it think that there is a face there, then the face icon doesn't show up, and you have no "face" to identify. The picture is never scanned again and, even if it were, Photos wouldn't see anything it didn't see the first time. So you cannot add this picture to a Person album. What we usually do is include the person's name in the Caption field. Then this picture will show up, along with all the ones in the Person album, when you do a search.
On a Mac, as I said, you can manually add a face and identity. I do this with pictures of people who are turned away, for instance. That picture will be put in the right Person album, though it is not used to add their features to Photos identification. The picture, synchronized with iCloud Photos, will appear in the iPhone's Person album. But this isn't available in iOS or iPadOS.
I don't know if you need this detail, but since I wrote it ages ago, I figure I might as well send it.
On a Mac, if a picture has an unrecognized face, you use stuff in the Info Window (⌘-i) to add the identifier. In the info window, below the Keywords field, is the Face ID field, and in there is a little + sign in a circle:

When you click on that, a little circle appears in the center of the picture, and you can resize it and move it to the face you want to record:

Then you enter the name, like Charley or Prince of Wales, or whatever. Then, if Charley has no People album, one will be created and this picture will go there. Later, if you need to change the name for some reason, you can do that in the People album, maybe making it King Charley III, or something.
The one problem we sometimes have is that the circle refuses to move, because Photos thinks you're still in the info window and want to drag the picture 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.
Does this work for you?