It can be used to prove ownership or identity by signing a Bitcoin message from private key of your known and used address, but it is not the only case to think of.
If you are the owner of that address and you own its private key then no body can claim it’s theirs. That’s the beauty of cryptos. Your keys your funds.
Someone can send you bitcoin without asking you, and it can be a fortune. It raises another concern, that if it is a mistaken sending, will you keep it or return it to the sender in such case, it depends on you.
As I'v said before