Prevent Search Engines from Adding My WordPress Site

Hey everyone! I have created a new site, and I am using a domain name (example,”www.yourname.com”), and it is registered with search engines, but, my WP site that I am using the domain name for is also appearing in search engines, and I don’t want both my domain name and my WP name to be on search engines, just my domain name.

Now, I know that there is an option in WP under Privacy where you can make it so that search engines can’t see the site, but it has been close to a week now, and it still has not disappeared? Should I wait longer, or do you think there is a problem?