You can easily move your cPanel website’s content to a different domain name by following the steps below:
Activate a new hosting plan or add a new domain in your hosting.
Upload the backup file with File Manager or FileZilla.
If the website uses a database, then create a new database and import a database backup. After that, you will only need to update the configuration file of your site. If the site displays an "Error establishing database connection", make sure to check this article, or this one if your site uses WordPress.
If you simply want to change the domain of your website but leave the content as it is (for example, you had domain.tld and want to have newawesomedomain.tld), and both domains are in the same hosting account, you would just need to copy the website files from one domain to another. A step-by-step guide for WordPress can be found here: How to Change WordPress Domain Name: A Step-by-Step Guide.
If your website has a domain mentioned in any configuration files (like OpenCart, Joomla, and many more), make sure to update the domain name in those files. You might need to contact a developer or a forum specified on your CMS for additional guidance.
If your website uses a database, and you are completely moving the content, you can simply continue using this database. If you want to have a copy of it for the new domain, all you need to do is:
Correct URL’s in a new database along with configuration file on your website.
Done, your site has been successfully moved! To see the changes, you may need to clear the browser cache and local DNS cache.