The following quotation indicates the origin of the name Aemilius:
"Numa gave to one of his four sons the name of Mamercus,
which was the name of one of the sons of Pythagoras
whence, as they say, sprang that ancient patrician family
of the Aemillii, for that the king gave him in sport the
surname of Aemilius, for his engaging and graceful manner
in speaking". --Plutarch's Life of Numa Pompilius
" is a root connected with both "music" and "honey".
Aemilius (or Aemilia
) means "s/he from whom music or honey come forth", i.e., "s/he of sweet or musical speech".