Access site using domain name instead of server name

Hi
I’ve read the well known articles on how to move wordpress to another server etc but I’m not sure exactly what’s required in my case.

I use a hosting provider for wordpress and I installed wordpress on the hosted machine so everywhere within wordpress this hostname is referenced, for example both the ‘wordpress url’ and ‘site url’ point to the hosted server name.

This wordpress site was created to replace an existing static website hosted on a different machine by the same hosting provider, but accessed through a domain name say ‘myownschoolwebsite.com’

So my hosting provider who also manages the domain name have pointed ‘myownschoolwebsite.com’ to the new wordpress website and this works fine, I can access it at ‘myownschoolwebsite.com’ However wordpress still uses the internal host name so any links are generated containing this hostname and not ‘myownschoolwebsite.com’ This means the address bar changes to the internal hostname once the home page is left.

Is there anything that I can do here so that wordpress will only use ‘myownschoolwebsite.com’? I don’t have access to cpanel by the way

Thanks!