Unless you use a DEX to swap and exchange bitcoin for other coins like Monero and then use another wallet to buy and receive bitcoin, the wallet will still be linked to the address that you send it to. If you ever want to trace that transaction, let's not forget that it's a public blockchain and transactions can be tracked by anyone who has access to the address on the blockchain.
 
There are means to clean up coins that you have already bought from the centralized exchange; either you can exchange them anonymously or you can send them back to the centralized exchange where you bought them and exchange them back to Fiat, where you can later use the fiat to buy from Dex P2P, where one will know what the funds were used for and only you will know what address and the amount of bitcoin that you hold.