Wait a few days longer and keep the iPhone plugged into a power supply, so it will scan the library.
we can only name faces, that Photos has detected. And Photos will scan a photo only once, unless we add adjustments. Then Photos might scan the photo again, but using the same algorithm, so it is unlikely it will find additional faces. Photos will also scan the photos again after a software upgrade, that has changed or improved the algorithm for the face detection.
If Photos has finished the scan for faces, but not detected the face, update the system on the iPhone, hoping for an improved face detection algorithm, but that might scan all images again for faces. If there is no update available, add the name of the person to the caption, or add the photo to an album with the name of the person. then a search will also find the photo.
If you are having a mac as well and are syncing the photos with iCloud Photos, you can add the face manually in Photos for Mac, and iCloud Photos will sync it to your iPhone.