With a Mac, you can tag any face, even if it's not recognized as a face by Photos. But on an iPhone, the name tagging only occurs for faces that Photos has already recognized to be faces. So profiles, maybe, and other faces it finds hard to recognize, are not shown. If it finds faces, you should see this:

Some faces have question marks, and you can tap on that face and add a name. Here you see a face with no question mark, and that's because it already knows the name.
If you have a Mac, then when you select a picture, you can use ⌘-i to bring up the info window. and in the lower left you will see a plus sign in a circle.

Clicking on that will bring up a circle on the picture. You can move the circle over the face you want to tag.

You may have to click once inside the circle to get its attention, but after you've moved it over the face, you can type the name, perhaps Prince of Wales or King Charles III, for instance. Then the king will show up in your people folder.
I started writing this before I realized you had asked about a phone, not a Mac. I thought I'd leave it, just in case...