How to change the primary domain name and keep the existing one pointed to the site?

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.

source: http://kb.siteground.com/article/I_would_like_to_change_my_primary_domain_name_however.html