There is a video floating around of a ThompsonFly 757 (?) which suffers a birdstrike on t/o. You can hear the ATC audio, and after the initial mayay call (spoken 3 times as per the book), the pilot and ATC prefix some transmissions with a single mayday. I'm not sure if this is written in procedure or law anywhere, but it sounds very sensible, particularly to keep unnecessary traffic (read: all other traffic) quiet.