changing domain name

Hi all,
I have developed a wordpress site on a host server using cPanel. Before the domain name was pointed at the new name servers I accesed the site using https://severname/~sitename, and this is the url I used to set up WordPress. Now that the domain has been pointed to the site, of course that’s what still shows up as the domain name.

I’ve read the information here about moving wordpress, but I was wondering, since I’m not moving any files, if I can just change the name in the general settings, or if there will be more to it than that?
Thanks for your help,
Jeff