That's a great question.
The short answer is yes, absolutely.
Remember, the way you prove ownership in a blockchain is by signing a message with your private key. That needs to be kept as safe as possible (Trezor and Ledger make it grandparent friendly).
Your public address is a part of the blockchain. You can view all public addresses of a blockchain at any time, using blockchain explorers like etherscan. It is not private, although you may prefer not to tell yours to people if you hold a lot in it.
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