Question: I started a VPN connection with `sudo openvpn --daemon --config connection.ovpn`. Is there a way to terminate this connection without using `ps` to search for the process and then `kill` it myself?

Answer: 
Since OpenVPN does not seem to offer any function of its own for this, you are probably looking for `pkill <process-name>`, which will search for *all* processes matching the given name, and kill them. 

If you got multiple instances running, but would like to kill only a specific one, the `-f` option allows you to match against the full process-call including parameters, e.g. `pkill -f "openvpn --config connection.ovpn"`.

See the output from `ps x` or `pgrep -lf <process-name>` (same as `pkill`, but doesn't kill them, so essentially similar to `ps | grep <name>`) to find out with which parameters the daemon was started.
No, you will need to kill the process. In fairness a daemon management script would do just that. You can use pgrep or pkill to make your life easier.