One of the stellar unique baby names from mythology, Andromeda was the beautiful daughter of Cassiopeia who, like her mother, literally became a star--the constellation that bears her name.The Bohemian Andromeda makes a dramatic and adventurous choice in a time when four-syllable mythological names are gradually making their way into the mainstream.
 Andromeda Tonks (nee Black), is a Harry Potter character
 Cousin name Andromache belonged to the tragic wife of the Trojan Hector, appeared in Shakespeare's Troilus and Cressida and was the subject of plays by Euripedes and Racine.

Andromeda

This name of the Cretan goddess of fertility is most popular now as the more melodic Ariana, but Ariadne has possibilities of its own. It first entered the US Top 1000 in 2014. The renewed interest in the name falls in line with the revival of other mythological names like Apollo and Athena. The trendy nickname Ari doesn't hurt either.
 In Greek mythology, she was the daughter of Minus who gave Theseus the thread by which he escaped from the labyrinth. After being deserted by him, she married Dionysus, the god of fertility, wine and drama

Ariadne

Astraea -- also found as Astraia -- is the Greek goddess of justice and innocence who became the constellation Virgo.  A more unusual form of the many star-related names, from Astra to Esther to Estelle to Stella, all on the rise. Astraea was the daughter of Astraeus, the god of the dusk, and Eos, the goddess of the dawn.

Astraea

Adrastea

Aglaea

Amphitrite

Cassiopeia, the name of a mythological mother who became a stellar constellation, is challenging but intriguing, and has all those softening Cass nicknames available. And with all names Cass-related trending, Cassiopeia may be an unusual route to a stylish name.

With the rise of other otherworldly and mythical choices, from Apollo to Jupiter to Juno, Cassiopeia may just feel more possible for mortals now than ever before in its long history.

Some sources say the meaning relates to the cassia berry or tree, and may be "cassia juice," making this a botanical as well as a mythological name.

Cassiopeia

Cytherea, a place-name that is the home of Aphrodite, seems stuck in ancient Greece. 

Cytherea

Chrysothemis

Deianira

Ephyre/ Corinthe

Hilara

Sister of Antigone and daughter of Oedipus in Greek mythology, Ismene's name is unlikely to make it in modern times because of its teasability factor.  Ismay or Esme would be better bets.

Ismene

Ilithyia

Iphimedea

Metaneira

Persephone is the esoteric name of the Greek mythological daughter of Zeus by Demeter, the queen of the harvest. After she was kidnapped by Hades to be Queen of the Underworld, it was decreed by Zeus that she would spend six months of the year with her mother, allowing crops to grow, and six in mourning, thus accounting for the seasons.
 Despite the mixed message of her mythological past, Persephone has a light and lyrical aura, and pleasant associations with springtime and the harvest; she was also goddess of spring growth. Persephone was seen in the Matrix movies, played by Monica Bellucci, and could make an interesting replacement for the overused Stephanie.
 Persephone's meaning is in dispute: While some sources give it as the worrisome "bringing death," others indicate that's it's associated with dark blue and with speaking. Persephone was called Kore in childhood; in Roman mythology, she is Proserpina.
 Persephone is popular on Nameberry, ranking in the Top 100.

Persephone

This name of a tragic figure in Greek mythology, the daughter of King Minos, sister of Ariadne and wife of Theseus, has a mysterious and intriguing appeal, and would make a dramatic choice.

 Phaedra has been a persistent theme in literature, both ancient and modern. There have been plays by Euripedes, Racine, Unamuno, and O'Neill, novels, poetry, operas and film--as recently as the 2011 Immortals starring Freida Pinto.
 One celebrity pulled a gender switch when she named her son Phaedra Bloom Forever.

Phaedra

Penthesilea

Semele

Themyscira

merrybells's list "Mythology (Girls)" of 21 great name ideas: Andromeda - Themyscira!