The anonymity is within using several addresses. Just use more than one.
Yep using a new address for every transaction could possibly lower the risk of finding your main wallet and your identity.
Your reali life identity is nowhere to be found in the blockchain. You will have access only to transaction IDs not your name, pseudonym, nickname is present there.
Your name could be only compromised if you use same address while dealing with bitcoin satellite service (where you have to register with your name) and someone will find this relation.