Hello,
The first thing you might want to do is upgrade to 2.2.15 or 2.3.0, which helps with server support (among other things). That being said transferring the site to a cPanel server isn't very difficult, but you can encounter some problems depending on how you do it.
I generally upload a zip file of the site to the public_html directory and extract it using cPanel/shell access. This minimizes file corruption during the upload, and puts everything where it needs to be (assuming the core is in webroot). Once uploaded you will want to verify the file/folder permissions are correct - if you extract a zip they normally get set correctly.
Once the files are in place make sure you update the config files (/config.inc.php, connectors/config.inc.php, manager/config.inc.php and core/config/config.inc.php). There are multiple paths that will need to be updated, not to mention your database information.
For the database I generally use the Database Setup Wizard in cPanel, the main reason ensuring everything gets created (user, database, and permissions). It's easy to forget a step, and yes I have forgotten them before despite too many MODX installs. The biggest problem I see is with the password being too weak, or containing special characters that could break it. Make sure your password lacks the ' or ; as they could cause you problems.
In regards to the usernames, I haven't had any problems with the cPanel prefixing to date. You can disable this in cPanel 11.44 if you want, but I wouldn't recommend it personally. Naturally, once the database is setup make sure you upload your sql file for the site.
Your install should run properly at this point in time, however you can also run the installer again in upgrade mode just to make sure everything is happy. Oh, and don't forget to delete the cache folder located in your core directory. We can't have an old cache breaking your shiny new site
Hope that helps