Any droplet you create will be assigned a public IP address but you could disable the public interface or restrict traffic once it is created. There are a few ways to do this:
1.) You can set up an iptables or ufw firewall to drop all traffic to your public IP
2.) You can use the command
ifdown eth0
to disable the public network on a one-time basis.
3.) You can comment out the configuration for the eth0 interface in your droplet's /etc/network/interfaces file.
If I disable public interface, how can I ssh in to access my host? Does that use a different interface? Will I still be able to access my host from the Digitalocean.com dashboard?
You will still be able to access your droplet via the web console. Your droplet sees the web console as a local keyboard and display so it is not dependent on networking. You can also ssh in through another droplet in the same data center on the private network.
as mentioned before you can disable eth0 and use private network to access your droplet. you have 2 options:
1) manually edit interfaces file in /etc/network/interfaces
sudo vi /etc/network/interfaces
here you just delete eth0 cfg block.
2) simply disable eth0 from command line
ifdown eth0