If you registered in any centralized exchanges, you linked your identity with your bitcoin address and probably to your entire financial BTC history.
1. How to stay anonymous when you buy and sell Bitcoin?
Don't worry, Binance and Kucoin exchange can withdraw 2 BTC daily without KYC. in this case you still anonymous.
2. How to anonymize Bitcoin if you purchased it from a centralized exchange?
Then, after you bought from Binance withdrawing your 2 BTC into Electrum or Coinomi wallet, in this case, you still anonymous if you didn't tell your address to everyone.