An Old Account and a New Username

I originally deleted an old Origin/EA account due to privacy concerns that I had with it.

To delete the account I initially started by changing the username, and then followed it through with a complete account removal. The problem that I am now facing is that when searching in Google the username of the original account shows up. To add to the problem, that account now links to my new account (the one I am posting from).

Is it possible to permanently delete my old account, and therefore prevent it from showing up in Google and other search engine listings.