MichiganWagon
kiwifarms.net
Your Private Key is your's unless you let it slip (ex: you emailed it to yourself and then your email account gets broken into).But then does the person who traced it back to you have any access to the private key portion (password)?
And to answer the original question, if Coinbase links your IRL ID to your bitcoin wallet, they (or anyone with that info) can search your transactions and link it back to your name. (disclosure: I don't use Coinbase and don't know how secure their servers are. But assume that they will eventually get hacked or get lawyer'd).