Initially when I set up the site , I had set up the hosting CPanel for a particular domain. Later I went and changed the CPanel to another domain name.
However the site does not show up when I type in the new domain name as the URL, it still gets redirected to the old domain name, and shows a "setup site" static page.
Is there any other change am supposed to do apart from just changing the domain name the CPanel set-up?
Depending on how you built your website it may be domain specific.
If you built a wordpress website there is a specific process that needs to be done to successfully change the domain.
Here is some info that should help you correct the site url discrepancy the "easy way"
@AHanda Based on your description is sounds like you may have been forwarding your new domain to your old domain. Now that your Domain has changed your cPanel account does not have an entry for the old domain and is redirecting to the setup page.
After changing your domain the next step would be to make sure your new domain is pointing to your cPanel IP Address.
Manage a forwarded domain use that link to make sure your domain is not being forwarded and delete any forwarding that may be setup.