I’ve found USUALLY, that if a host is using cPanel, Plesk, Helm, Direct Admin, Interworx, Layered Panel, Vdeck, or Ensim for a control panel, the database host/server is ‘localhost’

On one host, icdsoft.com, it’s localhost like this:
localhost:/tmp/mysql5.sock

Hosts using HSphere as a control panel usually are using variations of sql.hostname.com but on the screen where you view the database info, it will display the host/server name.

Network Solutions uses an IP address for the database.

Even though most Helm control panels hosts use localhost I’ve seen mysql.yourdomain.com:3307 as the host.

If you can’t figure out a database host, many times you can use phpMyAdmin to access the database and then the server name is usually displayed in phpMyAdmin (sometimes you have to click on Database link for the server name to appear).