There is no way to add faces manually Photos iOS.
However, when I add them on my Mac, they will sync with iCloud Photos to my iPhone and iPad as well.
For the time being, do it the old-fashioned way and write a list of names into the caption of the photo - left to right : Dad, Mom, Junior etc. Then you can look up the names and a search will find them as well.
I am sometimes duplicating a photo and are using mark-up to circle the missing faces on the copy of the photo and write the name below the face. Then a search for text will find the circled faces as well. This is very useful for group photos even on a Mac. Manually added faces tend to vanish after a major system upgrade, and then the copies of group photo with the circled faces will help to reassign the names years later, when I also do no longer know who's who.