Adding filename into file content

Dear Experts,

Please help to teach me how to add the filename into the file content.

Actually the file name are EVENTS-20050912.

New output that I want
EVENTS-20050912 03:33:37 ALARM: BTSSPAN-277-1 30-18013
EVENTS-20050912 12:10:28 ALARM: BTSSPAN-297-2 30-18013
EVENTS-20050912 20:40:05 ALARM: BTSSPAN-297-1 30-18013
EVENTS-20050912 23:55:27 ALARM: BTSSPAN-277-1 30-18013

**********************************************************

*My original data but didn't have file name into the content *

03:33:37 ALARM: BTSSPAN-277-1 30-18013
12:10:28 ALARM: BTSSPAN-297-2 30-18013
20:40:05 ALARM: BTSSPAN-297-1 30-18013
23:55:27 ALARM: BTSSPAN-277-1 30-18013

nawk '{$0 = FILENAME OFS $0; print}' myFile