"Eos" is not an acronym in the case of the faction names (therefore, "EoS" makes no sense); "Eos" and "Dione" are Greek theonyms.
In the case of Dione (Διώνη -- a three syllable word accented on the penult, or second-from-last syllable -- dee O nay), the name refers to an ancient Earth Goddess, perhaps equivalent to Gaia, who was, among other things, the Mother of Aphrodite (see Homer's Iliad), and likely a Queen of the Gods before Hera. Her name means simply "Goddess" (it is in fact the feminine form of the theonym "Zeus," which means "God").
Eos (┤╔ως -- a two syllable word accented on the penult, or second-from-last syllable -- EH ose -- where the second syllable does not rhyme with "pose" or the verb "close," but rather, with the adjective "close"), however, is the name of the Goddess of Dawn, also a primeval divinity, considered to be not Olympian, but Titan. There is a beautiful poetic image used consistently in both poetry and prose about her, but I'll refrain from posting it here, as it would be likely to be twisted into something inappropriate.