Yes, you will need to repoint you new vcenter to existing external PSC controller. The Topology will be like this.
You can perform the steps in KB as ITaaP has mentioned, for checking Site name you mentioned on both vCenter you can see http://www.virtuallyghetto.com/2015/04/vcenter-server-6-0-tidbits-part-2-what-is-my-sso-domain-name-site-name.html