Insane shower idea

2 Harry Potters!

Wrong boy who lived trope, except there is a mix up (like with adam in good omens) and both Petunia and the Potters think they have Harry Potter.

The real one (and boy who lived) goes to Petunia, the wrong one (who everyone thinks is Harry and grows up being called that) with the potters.

Magic is all about intent, so the wrong boy is actually identified as 'Harry Potter' too once everyone recognises that as his name.

Real Harry gets accused of being a glory theif at the sorting even though he didn't know magic existed until a week ago (no follow up letters or visit because fake 'Harry' had his)