Here are some of the "H" (eta) names — the seventh letter of the Ancient Greek alphabet —that were used for women in Ancient Greek society. Eta was originally similar to our letter H (the capital form is actually identical) but was later given the same sound as epsilon ('ay' sound), and in modern Greek is transliterated as 'i' alongside iota.
Most of the names found below have been taken from inscriptions and tomb reliefs.
The first six letters can be found in these previous posts:
Hedanthe
hedys "sweet, pleasant, agreeable" + anthos "flower"
Hedeia
hedys "sweet, pleasant, agreeable"
Hediste / Hedista
hedys "sweet, pleasant, agreeable"
Hedyle / Hedyline
hedys "sweet, pleasant, agreeable"
Hegema / Hegemone
hegemon "leader"
Hegemonis
hegemonis "imperial"
Hegenassa
hegemon "leader" + anassa "queen"
Hegesandra
hegemon "leader" + andros "man"
Hegesilla
hegemon "leader" + illa (diminutive suffix)
Hegesippe
hegemon "leader" + hippos "horse"
Hegestrata / Hegesistrate
hegemon "leader" + stratos "army"
Hegeso
hegemon "leader"
Heliodora
helios "sun" + doros "gift"
Hemera / Hemeira / Hemere
hemera "day" - Hemera was the name for the goddess of the day.
Hepis / Hepia
hepios "gentle"
Herais
dedicated to Hera
Herakleia
Hera + kleos "glory"
Herodoxe
Hera (or heros "hero") + doxa "glory, renown, honour"
Herophila
Hera + philos "love"
Herosanthe
Hera (or heros "hero") + anthos "flower"
Hesione
hêso "knowing"
Hesychia
hesychios "stillness, quiet, rest"
