If, after adding a new font, you end up wanting to rename it, you can do that by clicking on the font section. There at the top of the customizer near the publish button is a little pen icon. If you click that icon, you can changed the fonts name. This does not alter any styles or any other settings and is really only for your reference.

Note: For your changes to become permanent, you will have to hit the Publish button at the top of the customizer.