How to stop users seeing all databases by default

Here is the scenario. You have created a login called "Jane" and have not added to any server role. And you are 100% sure that she has not been given any permission on any database and she has no default database. Here is the statement you use:

CREATE LOGIN Jane
WITH PASSWORD = 'Pa$$w0rd'
, CHECK_POLICY = OFF;

Now she logs into SQL Server as below;

And she sees the object explore. Not only that she can expand the databases node and see databases.

Of course, she cannot go into a database and see the content but this is an issue for many cases, why should we let Jane to see even names of databases?

This becomes possible by default because of the Public server role. By default Public server role has permission on VIEW ANY DATABASE and all Logins are autmatically added to Public role.

If you need to stop this, change this permission like below (you can easily change this using GUI too).

DENY VIEW ANY DATABASE TO Public;

Now Jane cannot see even names of databases unless she has permission on it.