Remove addon domain from the addon slot from your cPanel > Addon domains.
Change the primary domain name for your account from currentname to addondomain name. This can be done from Help Desk > Domain name change.
Back up the website files for primary domain located in the public_html folder and then place them in another folder.
Move the files from the addon domain’s folder to your public_html directory.
Add primary domain to your addon slot from your cPanel > Addon domains.
Copy/restore the website files for primary domain to the newly created addon folder.