That is a hard question, with an answer worth lots of $$$.
But briefly saying- you got many methods to find a face in an image. Lets say you've used Viola & Jones, and got the face. You want to know who it belongs to, right? You must have a database, with tagged faces- faces encoded into some feature vector, labeled with names. Now, if a face found by a face detector is similar to one of the database elements- it is probably it. If not it is either a new person, or the face has undergone a change against which the feature vector is not robust (light, glasses, beard, mustache, haircut, pose scale etc..). Regarding the real question to be asked- what is the best feature space to use- a lecture given by Prof. Wolf on " Deep learning " presented very impressive results. Face recognition vai LBP works nicely. Google scholar is fool with papers. You need to choose and try some...