To protect your privacy and break the connection with KYC, you can use a bitcoin mixer e.g. chipmixer.com or better, mix through Monero (XMR). Monero has an obfuscated blockchain which means that no one can see who sent monero to who, when and what amount.
To mix with monero:
- Download the wallet from https://getmonero.org
- Make 1 monero wallet (keep the password, mnemonic and private keys safe)
- Convert bitcoin to monero with https://shapeshift.io and send it to your 1st wallet
- Make 2nd monero wallet and send your monero from your 1st wallet to your 2nd wallet -- this step breaks the link due to moneros obfuscated blockchain and RingCT
- Make a fresh bitcoin address
- Convert the monero from your 2nd wallet to BTC with https://xmr.to and send it to your new bitcoin address
Keep in mind that there will be a higher fee due to the exchanges (ca 5-10%) but it is worth it to protect your privacy.
For better privacy, you can run the monero wallet through tor (use torsocks command) and connect to a remote onion node.
Better yet just use Monero and convert to btc when needed, it's cheaper that way and you don't leave a trail of transactions that will look suspicious.