If you know the SPID of that particular user then use DBCC INPUTBUFFER or fn_get_sql as follows:-

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DECLARE @HANDLE BINARY(20)

SELECT @HANDLE = sql_handle from sys.sysprocesses where spid =

SELECT text FROM ::fn_get_sql(@handle)

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to get the text of the query, and then by that text u can know the database. How many user databases are there on that server?