Hi @jr5689. To further elaborate on @JustSomeTech’s post if you add your Domain to the system, nobody else would be able to do so.
Let’s assume you control exampledomain.com and you want to manage your DNS from your Digital Ocean’s control panel. To do so, you just need to add your domain to your account from your control panel. Once done, changing the Nameservers of the domain, will secure you control of it.
Once you’ve added your domain, nobody else would be able to add it in DigitalOcean’s system as it will create a DNS conflict.
Someone Added it before you did - Example
In the offchance someone added it before you and you can’t use it now. If you are able to prove you are the owner of the domain , you’ll be granted access/control over it.
There are means to prove your domain’s ownership and Digital Ocean will respect that.
All in all, there is no need to worry about someone else taking control over your domain. There are procedures in place to prevent that from happening.