URL simplification

We are using WP on a hosted domain. On that hosted domain we have an add-on domain, and that is where the WP is used.
It installed and is running fine.
Our question is regarding the URL shown in a browser when the site is visited. When we open the homepage in a browser, we get a URL such as: https://yourdomain.com, as expected. When we follow any links we get instead a URL with the IP address, such as: https://[IPaddress]~subdirectory/domain name/section/
This works, but I’d prefer to have a more discreet and friendly URL.
I contacted the hosting company, and they suggested going into the mySQL database table ‘wp_options’ and manually changing the ‘Site URL’ and ‘Home’ fields to what we wanted displayed in the browser URL display. That worked for solving that issue, but created other issues, such as as soon as we move off the homepage via a link on the homepage, we get a 500 error. Obviously, there’s more involved than those two fields.
Anyone know how complex this is going to get to be able to solve the first problem yet not upset the rest of the apple cart???