In this case we recommend the following steps:

1. Change your primary domain from your Customer's area > Manage (next to the account whose primary domain you wish to change) > Primary domain name change > Go.

You can also change your primary domain from your Customer's area > Get support > Report a hosting related issue > Domain name change;

     2. Park your old domain name in cPanel, Parked domains.

This will allow your site to work by both your old and new primary domain name.