data is the user which executs apache. You must be running the script through apache user on you machine. To do a chown you must be the owner or a super user try sudo chown -R. Or log into super-user mod type su - in your terminal then enter the root password. Beware as root you can do anything you have all rights, think twice before executing a commande.
[edit] I see that your script is in public_html -> this is tha apache folder for your user maybe that is why it has changed the script to www-data as owner.
try this sudo setfacl -R -m u:www-data:rwX -m u:myusername:rwX /home/myusername/public_html/mydomain.com/public/wp-content
to add you and www-data as uses