setup network share to allow access by computer name

I want to have a network share that is only able to be accessed from one computer and no other computers on the network.

I have tried to add computer Name $ to the permissions and security settings. When I do that there is no access to the share I can add a user to both and then I can get to the share but it is from all computers.

I have also tried adding a condition in advanced security for the user to be on the device and that does not work as well.

How would I set up the permissions and security settings so I can have the share only accessible from one computer?

Thanks

Kirk