1. Put a name to a face means that you recognize a person's face but you can't remember his/her name.

Can you put a name to the face in this photograph?

2. Put a face to a name means you recognize a person's name but you cannot recall what the person looks like.

I know this person by name but I can't remember what he looks like.

If somebody were to ask you: "What's the name of the guy who told you the story about a little frog?"

Then you would answer: "I cannot put a name to his face, it was a while back."

,but if somebody were to ask you: " Jack, do you remember who Jillian is?"

in this case we would say: 'i cannot put a face to her name at this moment."

:)