There are many different wallet services, and you can also create a wallet on your own computer, so keeping your identity safe in regards to the wallet will be more difficult.
Your question, however, seems to center more around keeping your larger online Bitcoin presence secret. Consider a few things:
First, many major payment processing sites, exchanges, etc. will require your real name and a photo ID.
Second, you can use tools such as the following at Blockchain.info to trace Bitcoin exchanges. You can't get the personal ID of the individual, but now you are on your way to tracing transactions from a particular address:
Personally, if I had a huge number of Bitcoins, I would keep most of them offline in a separate wallet, and then keep a smaller portion in a smaller wallet. That way, even if someone manages to trace and deduce your wallet, they will only have info on a small portion of your total holdings.
Here is a tutorial on creating separate Bitcoin wallets, in case you're interested.
How can I split my bitcoin wallet?