Change installation subdomain and make links display properly

I am facing the following problem:

My site runs on subdomain1.hostprovider.com and its url is https://www.sitename.com

I have started a new installation on subdomain2.hostprovider.com and what i need to do now is point https://www.sitename.com to subdomain2.

When i redirect the domain name to the new subdomain the site works fine but on the browser’s bar instead of seeing https://www.sitename.com/pageID I see subdomain2.hostprovider.com which is obviously not what I want.

I am pretty sure there is an easy fix for that but i can’t get my head around since I am relatively new with the whole site administration deal.

I am not even sure if this is a wordpress related issue or something i should change on cpanel. Could someone please point me to the right direction? ??