There's no way to rename your account (without creating a brand new one, which will not be linked to your current YouTube account).
But you can sign up for a different email address (not Gmail), and use it from your Gmail account.
Say you sign up for
firstname.lastname@example.org. Then you can set this address up as an alias to your Google account, and send mail from it from the Gmail web interface. Your friends will never know your current Gmail address (which I'm dying to know :).
- Sign up for an email address somewhere other than Gmail
- Set up forwarding to your current Gmail address
- Sign in to your Gmail account, click your image in the top right corner, then Account
- Add your new email address under "Change your associated email addresses. A verification email will be sent to your new address, and if forwarding is working correctly, the verification email will be delivered to your Gmail inbox. Click the link in the email.
- Click the gear icon in Gmail, then Settings
- Click Accounts and Import
- Look under Send mail as. If your new address is listed here, click make default. If not, click Add another email address you own and follow the instructions given.
This way you'll keep your current Gmail account (and its YouTube sibling), but you don't have to use that email address in your correspondence anymore.