But that's Cranky Kong, so it's not the same character.
That's a really obscure technicality that can easily be reasoned away.
Both characters are called Donkey Kong in their prime and are large ape creatures. Even though DK Jr is technically the modern DK. This is like Donkey Kong is more of a title than a name, something that holds significance beyond the individual. Hence why when Cranky Kong gets older and less capable for Donkey Konging he removes himself from the name and lets Jr become the Full DK.
I would say this is fairly similar to OoT Link and TP Link who are definitely not the same person and OoT even meets TP Link as an old Ghost to teach him his moves and give him advice. This is role that Cranky Kong takes in DKC as well.
And let's not go down the rabbit hole of if it even was Cranky. Some games claim Cranky is DK's father, others that he is his grandfather.
Brawl itself states that Original Donkey Kong is Modern DK's grandfather... which makes things even more confusing.
Ahh I've gotten off topic, but TLDR, if the two links can be considered similar enough to be alts of each other, then so can the two donkey kongs.