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@sevpants Okay, the DigitalOcean “Private Networking” is sadly a bad labeling. It is used for communication within the same data center if you have other servers there. It has nothing to do with VPN.
So you want to setup a VPN server, so you can tunnel the traffic from your computer thru your DigitalOcean server? You need to setup a VPN server on your droplet - here’s a tutorial for StrongSWAN: https://www.digitalocean.com/community/tutorials/how-to-set-up-an-ikev2-vpn-server-with-strongswan-on-ubuntu-16-04
As @hansen stated, you’re not buying anything other than an automated installation service from the site you’re referencing. They essentially deploy a Droplet with DigitalOcean, run an automated installer and then hand things over to you – that’s the general gist of how it works.
That said, from their wording, I can see how one would be confused. Also, despite what they state on their site (i.e. anonymous IP) – the IP isn’t anonymous. It can be traced back to DigitalOcean, as could any IP to any provider as ARIN/RIPE make this information public.
That said, me personally, I wouldn’t exactly trust any site that claims that a VPN will provide anonymity or censorship avoidance as it’s simply not true – whether it’s $3 or $300.
A VPN will encrypt traffic, yes, though it isn’t meant to provide 100% anonymity or prevent censorship. Where there’s a will, there’s a way. If someone higher up, somewhere, wants to monitor you, they can and will by any means necessary. Does that mean they will? No, not at all. I’m just stating that a VPN isn’t going to protect you 100% from everything.