Actually, there're a couple of DigitalOcean tutorials to complete this task.
How To Dockerise And Deploy Multiple WordPress Applications On Ubuntu
How To Configure Single and Multiple WordPress Site Settings with Nginx

Depending on your goal, you could use Multisite:
How To Set Up Multiple WordPress Sites Using Multisite

Please look at the existing tutorials before posting here.

It's actually pretty straight forward... just create a new directory for each site and install Wordpress on that sites directory... then configure your virtual hosts (Apache) or server blocks (Nginx) accordingly. I followed the DO tutorials and to be honest, no disrespect to the authors, but they were often lacking critical information that then needed hours of troubleshooting and Googling to resolve. Don't get me wrong, the DO tutorials are a great resource, as is this community, but I find some of the tutorials often jump around between different configurations and what not, and I personally found that they were often confusing.

Again, it isn't a reflection on the knowledge of the authors, as I think they are all actually great, but there is such an abundance of configurations available, such as several OS's, web servers, and a myriad of programs to install and settings to configure, that it really is a mammoth task to tailor tutorials to specific needs outside of just installing a specific item. A prime example is that you might be reading a tutorial about logging files and it jumps between different systems.. to those that have a reasonable understanding of what they are doing, they're great, for a total n00b, I would suggest perhaps not the best. I also found that some of the tutorials are a little dated now. Like I said, I personally found them to be a great resource, but for a n00b wanting to achieve things from beginning to end, don't be surprised if you also end up spending some "Google time" outside of the tutorials, when things don't work out exactly as planned.

As a side to the original poster, you're better off creating a droplet with a SSH key embedded from the get-go and don't do the one-click Wordpress install, mainly because the install of Wordpress takes mere seconds to do it manually anyways. Focus on the OS you are going to use as your first click, then focus on locking it down with the firewall and fail2ban (even if just SSH to start) and then move on to your server stack... again so many choices and different ways to go. IMHO, your first 5 minutes on a new server should be geared towards security... it's crazy how fast the hack attempts come flying in and it can be pretty disheartening spending hours following guides and getting everything installed, only to realize your server was compromised before you even managed to secure it.

Good luck with moving forward and if you need any help, I'm sure the community here will be a valuable resource for you.

According to this page, you must actually create a separate installation (I know, duh). If that is the case, I would imagine this would be a manual process since the image that came with the droplet already had one WordPress installation ready to go.

What I mean to say is, I think this would involve using SFTP to view the directory structure of your current blog, uploading a fresh copy of WordPress to a new directory (alongside the current one?). Then, creating a database, etc. From what I can tell, I don't think there is a "one-click" install for the same droplet that will install the same package on the same droplet. It looks like the process would be manual. Hopefully this is not the case, but from everything I see, that looks like it would be the only way.

I hesitate to suggest creating a separate droplet, but honestly that might be a better answer then trying to hack your way to a second one on the same droplet. I would not mind it much since I have this for years, but if you want a simple solution, a second droplet would be worth the extra cost.

I am sorry I could not be of more help.

You could try WordPress Multisite. It basically allows you to have multiple sites on one installation. Here's a tutorial for it but I would look into it first to make sure it would work for your specific use case. I use it all the time on $5 and $10 Droplets and it works perfectly.