How to deny access to see the logins in a database
Either if it's a Windows or SQL login, then by default, if it has only the PUBLIC role, won't be able to see anything except SA and himself. No other login (Windows or SQL) on the machine will be visible, if he hasn't some other server permissions.

Example for that behavior (both test logins have only the Public role):




So, if a login can see more than himself, it must've had some privileges assigned. It should be in the login properties.

Some other easy way to see it is by scripting the login: right click -> script login as - create to - and see if it has any server role assigned to it (role assignments are at the end of the script).