The answer
The exchange can know the destination it paid, and public blockchain data may reveal future transactions connected to that address.
What to do next
Use fresh receive addresses where practical and consider how UTXO consolidation can link otherwise separate funds. Never expect self-custody alone to create anonymity.
Sparrow Wallet
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BitBox Bitcoin hardware wallet
A Bitcoin self-custody device to compare; it does not make on-chain transactions anonymous or prevent address linking.
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Frequently asked questions
Will a hardware wallet erase exchange transaction records?
No. Custodial records and public on-chain payments remain separate from hardware key protection.