@mcj

Generally, the only requirement would be that you change the URL’s associated with the installation. This could be done from ./wp-admin or by using define() constructs which would be added to the ./wp-config.php file.

For example:

define('WP_HOME','http://example.com');
define('WP_SITEURL','http://example.com');

You’d change example.com to your domain on both.

You may need to modify your Apache VirtualHost as well if it was setup with a sub-domain, though if you’ve not touched the VirtualHost files, then you should only need to use the above to swap out the URL’s.

Before making the change, and so you have something to fall back on, I’d take a snapshot of the Droplet. That way if something goes wrong and you’re not able to fix it, you can restore from a snapshot.