I go by what's in the movie. That's why there's no debate about Phillip or Eric because they are referred to as such in the film. Failing that, The Encyclopedia of Walt Disney's Animated Characters (a massive tome for which 3 editions were made. It's not so much a dictionary, as much a comprehensive analysis of all animated films and works, including hybrids like Mary Poppins and Roger Rabbit) is my #1 official source.
BatB is tricky because Belle flat out calls to him "Beast!" at one point because the writer's never got around the answering that question. That book I mentioned just calls him "Prince / Beast". A CD-ROM is where he was first called "Adam" and its been used ever since, so I guess it is cannon now.
I don't take issue with people giving fan names for characters and acknowledging them as such. Passing them off as fact is what irks me, especially when rescources exist to prove otherwise.
People got Ferdinand confused because his name was mentioned in succession of Snow White and the Dwarfs. From there, people must have got that word confused with other names that start with F.