Part of the challenge to be a successful DBA is to use the tools at our disposal to answer these types of questions. There are [several] ways to answer your own question using batch files, PowerShell, SSMS, scripts, etc.
My batch file suggestion is only one possible way to accomplish this. I'll assume you have administrator access to all SQL Servers in your domain. Check dblist.txt on completion.
SQLCMD -Lc > serverlist.txt
FOR /F %%i IN (serverlist.txt) DO (
SQLCMD /S %%i /E /d master -o dblist.txt /Q"SET NOCOUNT ON SELECT SUBSTRING(@@SERVERNAME, 1, 30) AS ServerName, SUBSTRING([name],1,40) AS DBName FROM sysdatabases ORDER BY NAME SET NOCOUNT OFF;"