Hide SQL database from Management Studio

This actually won't work the way that makes sense or that you might expect that it would.

You REVOKE VIEW ANY DATABASE from the public role, but then the user has to be the database owner of the database or it can't be seen, but it still can be accessed.

The problem is a Database Engine Security shortcoming and not likely to be fixed in the current or future release of SQL Server.

Erland Sommarskog opened the following connect item for this a while ago, and it recently was discussed on twitter and with Microsoft by the SQL MVP's.

Vote for the connect and help make it more of a priority for Microsoft to fix:

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Basically the permissions are stored at the database level, so it would require enumerating each database to determine if the user has connect rights to display the database in the object explorer, which is an expensive task to perform and how the older EM used to do things.

The proposes solution is for this information to be maintained at the server level as well, which is a major change.

You would need to revoke the permission 'VIEW ANY DATABASE' from the role PUBLIC (SQL SERVER 2005 onwards)

There appears to be a server-side setting on MS SQL 2005 and 2008 to restrict the databases a user may see. I found the following text at sql-server-performance.com

In SQL Server 2005 it is possible with a new server side role that has been created. VIEW ANY DATABASE permission is a new, server-level permission. A login that is granted with this permission can see metadata that describes all databases, regardless of whether the login owns or can actually use a particular database. Please note By default, the VIEW ANY DATABASE permission is granted to the public role. Therefore, by default, every user that connects to an instance of SQL Server 2005 can see all databases in the instance.