It could be a random wizard or witch from another school. Maybe a student from Beauxbatons or Durmstrang who crosses paths with Harry before he meets Ron or Hermione. This could lead to a whole new set of adventures and friendships that change the course of the story as we know it.
One popular 'Harry Potter is someone else fanfiction' could be those that reimagine Harry as a different type of wizard, like a wizard from a different magical culture. For example, there might be fanfics where he is more in tune with the ancient magic of the druids.
Maybe he meets an exchange student from a different magical school. For example, a student from Beauxbatons or Durmstrang. They could share their different magical cultures and knowledge with Harry, and together they could face some challenges that require a combination of their unique skills.
They could go on an adventure to find a lost magical artifact. The two of them would have to face various obstacles, like dark creatures and complex spells set to protect the artifact.
Power and its implications are also common. If Harry has a new identity, it usually comes with different powers or limitations. Writers explore how he uses or struggles with these new powers. In some fictions, he may have to hide his powers to avoid danger, while in others, he uses them to change the wizarding world for the better.
Well, you might want to check out 'Harry's Double Life'. In this fanfic, Harry pretends to be a Muggle exchange student to investigate some mysterious events at Hogwarts.
If Harry meets someone else first, it could completely change his character development. For instance, if he meets a more cynical wizard at the start, he might become more guarded or less trusting compared to the Harry we know who met Ron and Hermione first.
In many of these fanfictions, Sirius Black could be an alternative caregiver. He was Harry's godfather, after all. He had a strong connection to Harry's father and would have been a natural choice to raise Harry if not for his imprisonment. He was brave and had a strong sense of family loyalty.
If Hermione's parents raised Harry, when Harry finally discovers the wizarding world, he might have a harder time adjusting as he's grown up in a very Muggle - centric environment. Also, Hermione's role in his life could be very different as she would be more like a sister in this scenario, which could lead to a very different kind of relationship between them and change the way they interact with Ron and other characters.