originally bird song was named aquila carmen — it literally translates to eagle song lmao. twilight picked it because aquila is one of the largest constellations in the night sky, and in Equestrian mythology represents strength and loyalty. and she's a nerd. rainbow thinks its dumb and cringey af, but theyd agreed beforehand: if it was a pegasus, dash could name them, if it was a unicorn, twilight could name them, and if it was an alicorn (as they expected) theyd come up with the name together. rainbow knew that twilight would pick some egghead name unfitting of a foal of a wonderbolt, and so felt pretty confident that she wouldnt get to pick — since they were so sure the kid was gonna be an alicorn…. but well… oopsie! aquila it was, and she had to deal with that
…however, as aquila learned to talk, it started to become apparent that she just can't pronounce her name lmao. even some adults couldnt seem to pronounce it, and it just made things super awkward — so, they had to come up with a suitable nickname for her.
Aquila had a big fascination with birds, and seemed to love that her name meant a big bird (even if she couldn't pronounce it). so they started to call her "their little birdie" or just "birdie" (or twilight did, rainbow would never admit to something as mushy as that….gosh…)
then after getting her cutie mark, it sort of sealed the deal, and they had her name legally changed to bird song. twilight still stands by the fact aquila was a good name tho. also heart stitcher finds out her name was aquila and thinks its the funniest thing ever and calls her that to piss her off