Which is why you would have to decide whether or not to use him vs the regular Toothless during certain battles, or, depending on your playing style/strategy, replace him entirely. It really doesn’t change the fact that he’s the same dragon.
In the end, this isn’t just a dragon fighting game. They’re sticking to canon lore as close as they can, it seems, with everything else (with obvious adjustments here and there) why would they break it with the biggest character of the entire franchise?
It would be like saying you want to see an episode of the series where Hiccup meets another Hiccup, only he’s wearing a funny hat. Just for the sake of…I don’t know, hilarious hijinks? It doesn’t have any explanation, it doesn’t fit in universe at all, and other than it being one of the character’s (let’s be honest it’s probably Tuffnut’s) fever dream, there’s no reason behind it.
I understand that you want to use a powerful dragon with another powerful dragon that you already have, but Toothless is still Toothless. He’s not a doppelganger, there’s no multiverse shenanigans at play. Just think of it this way: your original Toothless (purple) got into some paint, slathered it on, and now he’s ~Dreadfall~ Toothless; scourge of the archipelago (blue). No separation of being.