You can not do this easily as a user.
Windows provides an API which does not require elevated privileges to get this list of running processes: https://docs.microsoft.com/en-us/windows/desktop/api/Psapi/nf-psapi-enumprocesses
Technically you could hide your process by hooking (read: replacing) this API with a version that strips your app info, but this is a pretty substantial effort.
In Your Case
It sounds like from your comments that someone has remotely been able to take screenshots and get the process list. This is bad news. There are two primary cases:
- The game you are using has vulnerabilities which enable this this other person to execute some code on your machine.
- This person has somehow managed to install some kind of spyware on your machine.
Both are bad, and it isn't easy to figure out which is the case. I suggest removing the game and running your malware/spyware removal tool of choice (Windows Defender is a good start).