I believe you can create a wallet on Coinbase with just an email address and password.

If you are very concerned about privacy, you may need to provide more if you want to move USD into and out of the service. You could create a Coinbase account and move money into that wallet from another and you should be good to go.

Currently, Coinbase does send an email to the person you send bitcoin to with your account email address.

For privacy, we also recommend when you sign up for Coinbase that you do not use a personal or work email address. Instead use a Cloaked Email address, (an email privacy service Gliph provides), or a different throw away account.

edit: spelling