At the 1938 Oscars, Shirley Temple mentions the name "Ferdinand" among others while presenting Walt Disney his awards. Many have interpreted that she was referring to the Prince; thus, that Ferdinand is his name. However, she was not referring to him, but to another character, Ferdinand the Bull.
As confirmed by Dave Smith, Historian of the Walt Disney Studio Archives, the Prince was never given a name in the film and "Ferdinand" has never been used as one by the company.
The name "Florian" originates from this article. It was allegedly used by Disney when it started the Disney Princess franchise. This story is unproven.
There is an unproven story that there are documents in the Walt Disney Studio Archives that call the Prince "Frederick."
The Enchanted Stables collection reveals his white horse is a mare named "Astor."