Are transfers to MetaMask from an exchange anonymous?

How anonymous are transfers from an exchange (Binance, Coinbase) to a wallet (Metamask, Trust)? It looks to me like the transfer goes through a big, corporate wallet owned by the exchange when it’s transferred to Metamask. Is that the case?

That would mean that the only way that transaction would be linked to you is through non-public records the Exchange keeps, but not a personal wallet to personal wallet transaction someone could trace on Etherscan. In other words, the transaction is between my personal wallet and the Exchange as a whole, providing some level of anonymity.

Of course, this is assuming you haven’t publicly tied yourself to the wallet address on purpose (tweeting it) or accidentally (IP address, etc). That’s another conversation. Thanks!