Moving from IP address to domain name?

Hello.

I have a website that is in the process of changing hosts.

Currently I have setup the wordpress install in the new hosting account. The nameservers are still pointing at the old web host – so I am having to preview this new install using the server IP address..

With this setup, my WP blog is set to an address like this:
https://67.15.213.3/~user/

The concern I have, is when the nameservers switch. Will I need to go into the WP settings and change the blog homepage from ‘https://67.15.213.3/~user/’ to ‘www.thedomainname.com’? Are there any other issues I might run into?

Thanks!