Hiding your VPS' IP address is just security through obscurity and it's reccomended you always steer clear of these approaches, even though quite often they might be worth implementing anyway.
Ultimately your CPPS has a game client, which must connect to a game server, you can't hide the address. What you can do is make use of a reverse proxy to try and filter attacks, there are services online (which you pay for), which offer "DDoS protected" reverse proxies, as you would be pointing your game client to the proxy address, you would, in essence, be "hiding" your real game server IP.
There are also virtual server hosting providers such as OVH who provide DDoS protection as part of all of their plans (paid for by distributing the cost across all of their customers). Beware though, lots of hosting providers claim to be able to protect you from attacks, but can't, make sure to read up on reviews before getting ripped off.
You should read up on how to secure linux servers from different types of attack, before trying to setup any services which you run publicly, it only takes one google search to find out how to do things the correct way, and of course you're always welcome to make support topics here if you're stuck with anything.