Something seems to have changed for the worse in iOS 7. Under iOS 6, it used to be possible to select various "identifiers" (email, telephone number) to be used for FaceTime for the same person, and these could be labeled differently. In iOS 7, when adding FaceTime favorites, one is given the option of adding the contact for FaceTime or FaceTime audio, but it isn't clear how to add a specific identifier for a contact.
Unfortunately, there seems to be no easy solution to replace the iOS 6 functionality.
The simplest workaround seems to be to create multiple contacts for each point of contact you wish to differentiate.
Another possible workaround would be to add the different identifiers to 'favorites'. However, these will appear identical in favorites---same name & pic---so it would be difficult to differentiate.
(Based on personal experience and this related apple support thread)