Here are some of the "i" (iota) names — the ninth letter of the Ancient Greek alphabet —that were used for women in Ancient Greek society.
The ancient Attic pronounciation of the letter ι "iota" was as a short i (like thin) or a longer 'ee' sound. As with the letter epsilon, iota names are sometimes transliterated with a preceeding 'h' if there is a breathing mark.
Most of the names found below have been taken from inscriptions and tomb reliefs. As always, I've opted for more uncommon options, so no Isidora, Iris or Ianthe here.
The first eight letters can be found in these previous posts:
Iaso
iasis "healing, cure, remedy" - This was the name of the Greek goddess of healing and medicine, but also used for actual Greek women.
Iasonike
iasis "healing, cure, remedy" + nike "victory"
Iassa
"from Iasos (ancient city)"
Heira
hieros "holy, sacred, divine rites"
Hierodora
hieros "holy, sacred, divine rites" + doros "gift"
Hierokleia
hieros "holy, sacred, divine rites" + kleos "glory, fame, praise"
Hieronike
hieros "holy, sacred, divine rites" + nike "victory"
Hierothea
hieros "holy, sacred, divine rites" + thea "goddess, the gods"
Hierotima
hieros "holy, sacred, divine rites" + timao "to honour"
Hikane / Ikane
hiko "to arrive, competant, capable"
Hilara / Ilara
hilaros "cheerful"
Himeria / Imeria
himeros "desire, longing" - The feminine form of Himeros, a minor god who accompanied Aphrodite, but also the name of an ancient city in Turkey.
Hippaphesis
hippos "horse" + aphesis "letting go, deliverance, pardon"
Hippodameia / Hippodama / Hippodamia
hippos "horse" + damao "to tame" - Hippodameia was also a figure of mythology. grandmother of Agammemnon. It was also an alternate name of Briseis.
Hippokleia
hippos "horse" + kleos "glory, fame, praise"
Hipponika
hippos "horse" + nike "victory"
Hippostenis
hippos "horse" + sthenos "strength"
Hippostrate
hippos "horse" + stratos "army"
Hipponassa
hippos "horse" + anassa "queen"
Isagora
isos "equal" + agora "assembly, meeting place"
Isias
"daughter of Isis" - The name of a 1st century Queen of Commagene.
Isigeneia
Isis + geneia "born of, offspring, nation, kind"
Isidika
Isis+ dike "justice"
Isidota
Isis + dotos "gift"
Isothemis
isos "equal" + themis "order, divine law"
Isokrateia
isos "equal" + kratos "power"
Ionia
"from Ionia"
Iole
iole "violet"
Iphis
iphios "strong" - used )in both real life and mythology) as both a masculine and feminine.
Iphianassa
iphios "strong" + anassa "queen" - this name appears several times in mythology also. One is the daughter of Agamemnon and Clytaemnestra, sometimes considered the same as Iphigenia (Iphigeneia).
Iphigeneia
iphios "strong" + geneia "born of, offspring, nation, kind"
Ismena
isme "knowledge"
Ismenodora
isme "knowledge" or the River Ismeno + doros "gift"