In order to get a new IP address, you need to recreate the droplet. In order to retain your data, you can first take a snapshot of your existing droplet. You can do so by selecting the “Snapshots” tab in the server control panel.

Now, you can create a new droplet based on that snapshot. To do so, select the snapshot from the “My Snapshots” tab:

To make sure you get a new IP address, wait to destroy the initial droplet until after you create the new one. Usually people are more concerned with retaining their IP address, so the system will actually try to give you the same one if it is available.