It's true that renting hashrate for your DATUM gateway is like swapping your UTXOs for new ones coming directly from the coinbase transaction of OCEAN blocks, but there's very little privacy (if at all) considering all the information that Braiins sees (and what's public).

You can add several layers of obfuscation, like disabling worker names in your DATUM gateway and exposing it to the internet from an IP not linked to you. But even then someone who is continuously scraping the Braiins orderbook and the DATUM dashboard can notice when a new bid appears for the first time in Braiins and if a new miner pops up on the OCEAN dashboard with the same hashrate.

You can further obfuscate a bit by having multiple bids and using username modifiers (https://github.com/OCEAN-xyz/datum_gateway/blob/master/doc/usernames.md#username-modifiers-advanced) to distribute your hashrate among several reward addresses, but as you see there's no silver bullet.