Are you talking about an iPhone rather than a Mac? What iOS are you using?
The little circle in the Info Window indicates that Photos has scanned the picture, and Photos has recognized that the picture has a face in it. As you know, when you see that, you can attach a name to that face, and when Photos recognizes other faces with those features, it puts them all into a Person album.
On a Mac, for instance, in addition to the faces that Photos has recognized, you can circle a "face" that it hasn't recognized as a face, type in the name Jimmy, and that will be added to the Person list of Jimmys. Even so, that image is never used to find and identify other Jimmys, since it didn't have features that Photos understood t be a face. I do this on my Mac all the time when a picture shows the back of Jimmy's head, or when Jimmy's face is blurry or half hidden.
However, if you're talking about an iPhone, then there is no way to add a picture to a Person list if Photos didn't recognize that a face even appeared in the picture. If you would like for this picture to appear when you do a search for Jimmy, then you can add Jimmy's name to the Caption field in the Info Window. Then if you search for Jimmy, the Caption Jimmy and the Person picks of Jimmy will all show up.
I agree that it's unfortunate that you can't add unrecognized faces to the Person list. It might be added in the future, especially if you tell Apple that you think it's a good idea. Do the here:
Feedback - Photos - Apple