Instead of the proposed methods, you can log in while another user is logged in and start a new session instead of sharing the screen. This will not be visible or accessible to the local user. Use
vnc://<mac name or ip> from the Connect window in Finder to connect to the system. I’m not sure if I can permanently upload an image, but the dialog shown will be asking you if you want to share the other user’s session or login to a new one as yourself. This only works if the local user is not the same as the user you are trying to login to.
This works much like fast user switching, but instead of switching accounts locally, you can use them concurrently, locally and remotely! This also means that you could walk up to the computer and log out the current user or return to the login window and you will see yourself listed as currently logged in. This also allows you to locally take over your remote session if you wanted to.
Remote Access outside of the network
If you need remote access from outside of the network, it's a different deal. And if you don't know the address either, it's a problem too. The functionality you are proposing is usually used in business networks where there is a local administrative system in place. If you only have a single system somewhere remote (i.e. a single Mac somewhere in a house), you might be able to deal with it using iCloud, with the "Back to my Mac" feature. Another way would be port forwarding the VNC connection, but that leave a huge security hole, and is not recommended. You can also use SSH tunnels, meaning you only have to leave open the SSH port, and then in the command line you simply forward the remote VPN port over that secure connection, like this:
ssh user@mac-somewhere-else -L1234:localhost:5900
Then, while you leave that open in the terminal, you use
vnc://localhost:1234 in the Finder's Connect To dialog (Command-K) and this will use the SSH tunnel to the other Mac.
However, if you are targeting many remote machines or mobile machines or systems that you cannot access directly, you will need a special agent installed that uses NAT traversal via a third party service. Previously mentioned tools do this, i.e. LogMeIn, TeamViewer and similar types.
If you have multiple remote networks to access regularly, consider using VPN connections. This allows you to connect to the network remotely and access the resources within.
A third alternative for accessing remote networks is using a jump box or bastion host. It could be a simple Mac Mini that has a static IP address and SSH (or maybe even VPN) and you first log in to that and tunnel VNC to it. Next, on that Mac, you use the Finder's sidebar to automatically discover all the other systems in the network.
To have a better set of options to solve this, we will need more information on the use cases and what networks etc. you actually want to connect to.