Yes you are correct, DO just provides free DNS services for your droplet. You are still going to need to pay your registrar for the domain even if you use DO’s DNS, hope this helps.

Hi, @propermilano

Digital Ocean at the moment does no offer domain registration services, e.g DO is not a registrar. You will need to purchase a domain name from a third party provider and then use with your DO services.

Hope that this helps!
Regards,
Alex