First off, I'm sorry for the delayed response.
As to your question, I had to look through the code a bit as that's not a question we've had before, but makes total sense. Unfortunately though, no, there isn't currently a way to override the name of the login provider for display purposes.
That shouldn't be an overly difficult feature to add in a future release and I've added this to our development list.
Thanks,
Alex
change Azure to Microsoft
