Yoshi becomes Mario with the Mario Hat which still makes him Yoshi cause it's just a power up.
The Double Cherry just makes another Yoshi Mario
The Princess Crown doesn't turn you into Peach, it just makes you into a lookalike. The only confusion here is that you look like Peach (which ironically is just how the Mario Hat works).
Now with Cappy is still just Yoshi (Mario Clone) taking over Yoshi (Mario/Peach crowned) in the end they are still Yoshi the biggest concern is that Yoshi (the Clone) took over his own brain...