Try using cryptocurrency mixer or bitcoin mixer usually that's the service people use when they wanted to do an anonymous transaction or sending it to private address. Also, there is a wallet with a built-in Bitcoin mixer I think that was Wasabi wallet. I'm quite curious too what could be the other way to hide the transaction.
There's still a good mixer today that allows you to transact and remain anonymous but the effort of doing this is not easy for sure and you have to understand the system first before doing this. I didn't try to withdraw huge amount of money but seriously, of all the transactions that I have I don't think I can still transact on Private especially I'm more on P2P in Binance. This is a good question btw and maybe there's still a solution.
When we use P2P in Binance, that well enough for us to stay anonymous and only the seller will know our data, and of course, Binance will know about that. For most people who do not have big money, using P2P in Binance can be a solution to get their profit and they do not have to tell others about what they did. But for people who have a lot of bitcoin and want to stay anonymous, I am sure they will figure it out by themselves and who knows, they already have the way to hide their identity from others.