Nope, but now I'm wondering it :P I daresay she learned what his real name was and called him that, but because there haven't been any sequels with him as a human, we don't know what his name is.

We don't know.

A CD-ROM game[1] said "The Prince's name is Adam."
link)

His name is Adam. Here is a question for you. When did she start calling him Beast? Everybody else just calls him Master. Did he just say "You can call me Beast" as his way of introducing himself? Or did she just started calling him Beast and he went allow with it and didn't care much because he didn't want to give his real name yet because it made him feel more angry on not being human? I always thought of that as much as I did if she ever called him by his real name after the spell was broken. But I think she did. I like to believe she just decided to call him Beast just to call him something up until the spell was broken.

@MrsEmmaPeel she called him Beast when he was climbing up to the balcony she was on towards the end before he got stabbed. he said, "Belle!" and she said, "Beast!"

Defenitley!

Belle will call him Beast.