You have a nice setup that opens all kinds of possibilities. Can either Harry/Harri defeat Voldemort in this universe? And what will be the interaction between the two? My first reaction would be that the two would sympathize with the other, but would having some one else know you that well become annoying? ANd of course the fact that the two are different genders may have skewed how they were raised. You could go either way, that Harri was dopted on or abused by the Dursleys.
Author's response
There is no Voldemort in this universe... Tomasina Marvala Riddle didn't anagramize... though she does have a nom de garre...
Can Harry/Harri defeat her? Maybe.
Harry/Harri aren't going to be best buds, they are too alike and will grate on each other. They most certainly won't be lovers like a perv or two have requested. they will cooperate with each other.
For the purposes of this fic, this universe has humanity in a matriarchal society, with names following the mother's line. Harri's parents were Jane Potter and Lewis Evans.
SO, this universes Dursleys (Verna and Philip) treated Harri almost exactly like Petunia and Vernon treated Harry.