If you sign in with your email, that is your Skype ID for all intents and purposes. Mine is the same way and has worked fine for all interviews. Don’t worry! As for the interviewer not adding you yet, that’s normal for some schools.
I had issues at the time of my interview with the interviewer finding me. She promptly emailed me and asked for me to add her which resolved the issue. Moral of the story, have your email open and keep refreshing if you run into any issues.