If you want to change the domain name associated with the WordPress installation (site) you need to update the references for the old/current domain name to match the new domain name. This is usually only in the database, but sometimes there are some hardcoded references in the files as well, so this is something to keep in mind.
The process is not that complicated and you can also use plugins in order to complete the task.
Note:Please before you proceed take a snapshot of the droplet and also create a backup of the site (both files and database). This will ensure that if something goes wrong you can easily restore your site or droplet if needed
There are few ways to update the references in your database and it’s totally up to you which one you’ll choose. You can either change them manually if they’re not many or use an automation tool like plugin or external app.
One of the external apps that I’ve used and I know for sure that it’s working okay is: https://interconnectit.com/products/search-and-replace-for-wordpress-
You need to upload the script in your public_html folder and access it your browser, then you’ll need to fill your database details and enter the old name (IP address) and the domain name you want to use. Then you can first use the dry-run option and if there are references that need to be updated you can then run the script and update them.
Also an alternative way is to use a plugin called “Duplicator” it will update all of the paths and references from the current domain to the new domain. You can also use a plugin called: Duplicator. The plugin will generate a backup for your website’s files and database. Then when you import the files to the new domain, all of the references for the old domain name will be updated properly with the correct ones.
Another option is to use the All-in-One WP Migration plugin. The plugin will do the replacement for you during import. You do not need to use any additional database search and replace
Once this is done you can check the site for any errors as there might be some hardcoded references for the IP address in the files like paths to directories, files and etc.
Hope this helps!