You wont need a new WP account.
I’m not a cpanel user, but i imagine it has the facility to import a database previously exported from your original cpanel… Just ensure the new host, user, password and database name are correctly referenced in the config file and you should be good to go.
So really, to re-iterate, moving is a two step process, moving the ‘wordpress’ directory (folder) and all it’s contents and secondly exporting and inporting of the relevant database.
Hope this helps.