True, River knows his name, but no one else and no one in the current time period. I assume she had to know his name for their wedding ceremony. I'm sure she's his wife from the future. :)

The closest to Superman would be the other people from Krypton knowing his real name, ie his cousin, his now dead aunt and uncle, and so on. But unlike the Doctor who does not tell people his name, Superman hasn't been so reticent. Wonder Woman has called him Kal on a number of occasions and isn't the only one.

It's an interesting comparison, but not airtight. ;)