Here are some of the "E" (epsilon) names — the fifth letter of the Ancient Greek alphabet —that were used for women in Ancient Greek society.
Most are taken from inscriptions and tomb reliefs, though I have listed only those that are not commonly used today, so no Eirene, Eulalia, Elena or Eudora.
I have also included pronunciations (standard as taught for Ancient Greek in English) apart from those which are very intuitive to English speakers, the key to which can be found here. Certain names beginning with the letter ε (epsilon) are preceeded by a breathing mark, which is usually transliterated as starting with a 'h' (e.g. Ἑλενα becomes Helena; ‘Ερμιονη becomes Hermione).
The first four letters can be found in these three previous posts:
A B/G D
Eidothea (ay-dō-thee-a)
eidō "knowing, seeing" + thea "goddess"
Hekataia (hek-a-tī-a)
"belonging to Hekate"
Elaphia
elaphi "deer"
Elaphina
elaphina "doe"
Eleutheris (el-yoo-the-ris)
eleutheria "liberty, freedom"
Heliko (hel-ik-ō)
'elikos "to turn around, spiral"
Hellenokrateia (hel-en-ō-krat-ay-a)
Hellas “Greece” + kratos "strength, power"
Elpinike (el-pi-ni-keh)
elpis "hope, expectation" + nike "victory"
Empedia (em-ped-ee-a)
empedos "steadfast"
Empedokleia (em-ped-ō-klay-a)
empedos "steadfast" + kleos "renown, glory"
Empedonika (em-ped-ō-ni-ka)
empedos "steadfast" + nike "victory"
Empeiria (em-pay-ree-a)
empeiria “experience, adeptness”
Exaineta (ex-ī-net-a)
eks “out of, from, beyond” + ainetos "praiseworthy"
Epainista (ep-ī-nis-ta)
epainos "commendation, praise" + istes "concerned with, one who is"
Eparchis (ep-ar-kis) -- The 'ch' is technically aspirated as in the Scottish 'loch'
epi "over, above" + archos "ruler"
Epaphrodisia
epaphrodisia "loveliness"
Epaphrodita
epaphroditos "lovely, charming"
Epianassa
epi "over, above" + anassa "queen"
Epimeleia (ep-ee-mel-ay-a)
epimeleia "care, attention"
Epinike (ep-ee-ni-keh)
epi "over, above" + nike "victory"
Epicharis (ep-ee-ka-ris) -- The 'ch' is technically aspirated as in the Scottish 'loch'
epi "over, above" + charis "grace"
Epistheneia (ep-is-the-nay-a)
epi "over, above" + sthenos "vigour, strength"
Erata
eratos "the lovely one, beloved"
Eratonassa
eratos "the lovely, beloved" + anassa "queen"
Hermaia (her-mī-a)/ Hermais (her-mī-is)
"of Hermes"
Hermogeneia (her-mō-gen-ay-a)
Hermes + genos "born of"
Hermoxene (her-mōks-en-eh)
Hermes + xenos "foreign, stranger" -- perhaps a reference to an imported cult of Hermes.
Etearchis (et-ee-ar-kis)
eteos "truth" + archos "leader"
Eteokleia (et-ee-ō-klay-a)
eteos "truth" + kleos "renown, glory"
Evaineta (ev-ī-net-a)
eu "good" + ainetos ""praiseworthy"
Evameria (ev-a-meh-ree-a)
eu "good" + meros "part, share, portion"
Evanassa
eu "good" + anassa "queen"
Evarista
eu "good" + aristos "best"
Euthenia
euthenia "prosperity, abundance"
Eukleia (eeyoo-klay-a)
eu "good" + kleos "renown, glory"
Eumeneia (eeyoo-men-ay-a)
eumeneia "benevolence"
Eumetis (eeyoo-met-is)
eu "good" + metis "wisdom, skill"
Eunoia (eeyoo-noy-a)
eunoia "goodwill, beautiful thinking"
Euporia
euporia "prosperity, plenty, riches"
Eupraxis / Eupraxia
eupraxis "right thinking"
Eutaxia
eu "good" + taxis "order, rank"
Eucharis (eeyoo-ka-ris)
eu "good" + charis "grace"
Ephesia
"from Ephesus"
*Scientifically, and commonly in translaterations, names beginning with Ευ (Eu) followed by a vowel are pronounced as a 'v'.