My URL shows my host not my personalised one

I use a UK host company, myzen. I want all my pages only to show my personal URL ggsolicitor.co.uk not the host url myzen.co.uk. All the pages exist in both URLs with the same content but if I browse to ggsolicitor.co.uk all the internal links and pages browse to myzen.co.uk. Likewise when doing Google searches the results have the myzen references. How do I change this so that only the ggsolicitor URLs are shown everywhere?