First, you don't receive the extension number on an incoming call (the telephone system just doesn't work that way), so the phone can't display it. (And if you have 5 contacts with the same phone number, all of them will show up as just that number - and the first contact for the number.) And there's no way of changing that - the information just isn't sent to the called phone.
I tried 2 ways of adding an extension - both worked:
1. Add the contact, but put a # after the number, then the extension number. Add another contact, same number, also with a #, then that contact's extension number. You can choose the outgoing call but, as I said, the phone will display the first contact with that number.
2. Make the phone number button "Custom" and put in the person's name. Do the # thing, as above.
Add another phone number. Change that button to Custom also, and put in the next person's name. Put in that person's phone number and extension. (Again, incoming calls will show the name of the contact, not the name on the button.)
In either case, when you get to the point that the equipment at the number you're calling will accept the extension number, tap "Send".