There are several ways you can change the name on an incorrectly tagged Person. (Monte's method will only delete the name tag without replacing it with the correct one.)
Probably the easiest way is to do the following:
- Make sure People Recognition is turned on in the View menu
- Double-click the image so that it displays in single-image view
- Hover over the mistakenly named face (a circle with the named text box should appear)
- Click in the text box and edit the name
- Press Enter (the new name will replace the old one)

Note that once you start typing, suggested names will pop up and you can click on them. If the name has not previously been tagged, you will be asked to confirm the name I believe.