 Anath

 Louhi

In Semitic mythology, Anat was the goddess of fertility, hunting, and war.

Anat

In Greek mytholgy, Antigone was the noble and courageous daughter of Oedipus, who acts as his guide after he blinds himself. Antigone is also the eponymous heroine of a play by Jean Anouilh.
 Despite her heroism, however, Antigone has not yet made it into the modern world, but with the increasing acceptance of longer, weightier Greek and Roman names, this could change.

Antigone

Artemis, one of the key figures of the female Greek pantheon, is the ancient virgin goddess of the hunt, wilderness, animals, childbirth, and a protector of young girls, later associated with the moon. Artemis is the equivalent to the Roman Diana, but a fresher and more distinctive, if offbeat, choice. 
 Artemis was the twin sister of Apollo, one of the twelve deities who lived on Mount Olympus. She features in three of the fifth century plays of Euripides. The meaning of the name is largely unknown, but it's related to two Greek words meaning safe or butcher, not nearly as lyrical as her mythological story.
 Artemas, on the other hand, is a male name, though some gender confusion could arise from the Artemis Fowl novels.

Artemis

Atalanta was a beautiful mythological maiden who refused to marry any man who couldn't beat her in a footrace -- quite a role model. This myth is found in Ovid's Metamorphoses and later in Swinburne's Atalantis in Calydon.
 The addition of a fourth 'a' takes this out of the area of place names into a more rhythmic and romantic realm.

Atalanta

Basthet

In Greek myth, Circe, daughter of Helios, the sun, was a sorceress living on the island of Aeaea, who could turn men into animals with her magic wand, which is just what she did to Odysseus's crew in Homer's Odyssey, transforming them into swine. All was forgiven, however, as Circe and Odysseus later had a child together&mdash;Telegonus.

The name and legend have appeared in countless forms, from a section of James Joyce's Ulysses to short stories by Julio Cortazar to Toni Morrison's Song of Solomon to films to DC comics to a dance by Martha Graham.

So is Circe's seductive legend too powerful for a modern little girl to carry? Your call.

Circe

In Greek legend Clytemnestra was the wife of Agamemnon, mother of Orestes and Electra. She took a lover while her husband was away fighting in the Trojan War, and upon his return she had him killed as revenge for his sacrifice of their daughter Iphigenia. She was subsequently killed by Orestes.

Clytemnestra

Durga

Gaea

Gordafarid 

The mother goddess Ishtar (also called, or identified with, Ashtoreth, Ashtoret, Astarte and Inanna) was worshipped by the Assyrians and Babylonians as the goddess of love, war, justice and fertility. While the original meaning is unknown, the name possibly derives from "Attar" meaning the morning star. She has been equated with the Greek Aphrodite.

Ishtar

The Mayan goddess of the moon, also associated with love, pregnancy, medicine, and water.

Ixchel

Mythological princess who killed her kids. Eternal no-no. 

Medea

The mythological Morrigan was the ancient goddess of war, often symbolized by a crow.  Besides being a name, this is also used as a proper noun preceded by an article: the Morrigan, defined as a monster in female form.  

The meaning of Morrigan has been related to both terror and greatness.  While some relate the name to Morgan of the Arthurian legends, Morrigan and Morgan are actually unrelated.

Morrigan

Mami Wata

Mazu

Ostara

This Hindu goddess name is very popular in India. The goddess of love, fertility and devotion, representing female force, Parvati is the wife of Shiva and the mother of Ganesh. There is a Harry Potter character named Parvati Patil, a twin sister of Padma..

Parvati

Pele is a female name in Hawaiian culture that could make a provocative choice for a modern girls. Others might think you named your daughter after the all-time great soccer player, but the simple, rare, and lovely name Pele has mythological roots.

Pele

Scheherazade -- or Sheherazade --is a legendary Persian queen immortalized as the narrator of all one thousand stories in the One Thousand and One Nights. Her story is even more remarkable than the tales she tells.
Each day the king marries a new woman and then beheads her in the morning. Scheherazade volunteers to marry the King. She relates a gripping story and times it so that as dawn approaches, the King is left with a cliffhanger. Eager to hear the end of the story, the King spares her life. The next night, Scheherazade finishes the tale and begins a new one, again ending the night with a cliffhanger. And so on. After 1001 nights (and 1000 stories) Scheherazade tells the King she has no more stories. However, by this time the King has fallen in love with Scheherazade and makes her his Queen.
 Scheherazade is a long and weighty name, but on the right girl or woman it would be an unusual and wonderful choice. Another spelling is Sheherazade.

Scheherazade

Tiamat

Yemaya

LenaBlueBird 's list "Powerful female names from mythology " of 24 great name ideas:  Anath - Yemaya!