How do you cope with Database Server Inventory Management
I don't have direct experience with this task but know how folks get around this problem. :-) 

You setup some monitoring program to look out for all SQL Server instances on the network and anytime something comes up that is NOT in your radar, you can catch them right away. There are lot of options and here are couple of them. I am pretty there might be others or many variants of these two.

http://www.straightpathsql.com/archives/2009/02/what-sql-instances-are-installed-on-my-network/

http://andrekamman.com/find-sql-servers-on-your-network-with-powershell

That said, I have to tell you that if someone brings an instance without notifying the DBA or production support team then this should be handled politically. Get your boss (in confidence) to talk to their boss and avoid future recurrence of the problem. GL.