To ensure your new primary domain name is used, you should first park the previous primary one and then redirect the old domain name to your new one by inserting this code to the .htacess file in your public_html folder:
RewriteRule (.*) [R=301,L]
You should replace in the above code with your actual domain name.
In addition to the redirect we would suggest that you contact every backlinking site to modify their backlink to point to your new domain.