It's pretty common when someone sent you something by mistake and in this case cryptos. People make mistakes such as that but it never happened to me before. I mean, I might send them back to the sender's address. Or maybe the rightful owner will make some announcement saying they want their money back and they can provide proof that it's theirs and accidentally sent to the wrong address. Nonetheless to say, some might just keep them in their waller lmao. Well, your call.
Newcomers into crypto usually make mistakes because of their lack of education. With many wallets adopting a user-friendly interface, mistakes are often a rarity these days. The only way someone would mistakenly send you 1 ETH is if the address has been typed manually. Scanning QR codes or NFC tags avoids this problem. But for reasons unknown, some people prefer to type in addresses manually for sending coins across the Blockchain. If you receive free ETH by mistake, you can either keep it yourself or send it back to its original owner. The fact that crypto/Blockchain tech is decentralized, allows anyone to do as they wish with funds confirmed on-chain. That's not the case with centralized payment processors like PayPal or Skrill.
As long as you put the coins to good use, nothing else matters. I'd personally donate the 1 ETH to a charity of my choice by exchanging it to Fiat. If you're planning to send coins back to its original owner, then ask for a transaction hash along with a signed message from the address where the funds originated from to prove ownership. It'll be quite challenging for the owner to contact you directly since addresses have no identities linked to them. But if you publicly disclose your addresses along with your contact info, it'll be much easier for the owner to claim the funds back from you. Whatever you do with the coins receive by mistake, it's your call. Just my thoughts