iPhoto tagged wrong person

To be able to see the circle around the face with the name below it, you have to enable "Show Face names" in the "View" menu. You can then directly type the correct name into the textfield below the faces circle.

You can also reject a wrong name, while viewing the People album of the person. Set the View to "Faces", not "Photos". Then ctrl-click any face in the album that is wrong and use the command "This is not ...".

Do you mean that Photos has seen John's face and tagged it as Matt? If that's the case, you can Control-click on the tagged face in the picture and it will let you click "This is not John" and you can then re-name. Like this: