You can use the un-documented SP "sp_MSforeachdb" for this

IF OBJECT_ID('tempdb..#tmp_Indexes') IS NOT NULL

DROP TABLE #tmp_Indexes

DECLARE@strSQLVARCHAR(2000)

DECLARE@IndexName VARCHAR(1000)

CREATE TABLE #tmp_Indexes

(

DatabaseNameVARCHAR(100),

IndexNameVARCHAR(1000)

)

SET@IndexName = 'mst_Employees_IX01' -- You can enter the name of the index here

SET@strSQL = ' SELECT ''?'', name FROM ?..sysindexes WHERE name LIKE ''%' + @IndexName + '%'' '

INSERT#tmp_Indexes( DatabaseName, IndexName )

EXECUTE sp_MSforeachdb @strSQL

SELECT * FROM #tmp_Indexes

IF OBJECT_ID('tempdb..#tmp_Indexes') IS NOT NULL

DROP TABLE #tmp_Indexes

Edit: Added a comment in the code