Possible, but unlikely, as there's been no mention of a previous Ganondorf/Ganon in any existing games... even if it wasn't publically known, the royal family would almost certainly have kept a record of him in case he returned, so wouldn't have trusted Ganondorf like they did at the start of OoT.... they done this with Demise in Skyward Sword, and most other appearances of Ganon refer to his previous encounters.
Well, the Old Man talks about this CG creature like he doesn't know what this it is, which is strange, if Ganon has been showing up regularly in history. Even in the DT he shows up regularly. That's one of the things that makes me wonder if this isn't just slightly revealed new lore that we are going to see that is new stuff about Ganon.
(I'm betting that there will be a 'long lost' addendum to HH published eventually. They would have to, to include any new games and other stuff made after it came out.)
Now as to whether people would trust a man named
Ganondorf if Ganon has showed up prior, well, the RF trusted him despite him being known as the
King of Thieves and Zelda explicitly saying the man had evil looking eyes. Plus most of the Gerudo women
still trusted him despite the fact that he murdered his own followers when he found the TF (and it's got to have gotten out that he murdered them, or somebody wouldn't be saying it.)
If that many people still trusted this man despite the crap ton of red flags he was giving off (even kneeling right in front of the king he has a gleeful evil look plastered on his face) having part of his name contain 'Ganon' probably wouldn't be enough of a deal breaker that people are making it out to be. It would be a strangely low bar all of a sudden when all of the other stuff didn't even seem to be enough to make people go 'Hmmm, I don't think I trust that man...'