We all know the planets, and some are brave enough to use Venus, Mercury, Mars, and even Jupiter or Neptune on their bundle of joy. Some get creative and use names from other languages, such as Sol or Soleil. Some parents use different names associated with the moon - Selene, Luna, Phoebe. Let's look at the other starry baby name options; names used for the moons of other planets, dwarf planets, stars or constellations can be just as celestially appealing.
Many things in space were named after characters in Shakespeare, Pope, Spencer and other literature, named after real people (especially those that discovered the object in space), and Greek and Roman mythology (sometimes other, older mythology as well).
Stars with proper names that have been or could be used as baby names: Alcyone, Capella, Altair, Aludra, Alula, Ascella, Alya, Atlas, Bellatrix, Castor, Chara, Electra, Eltanin, Izar, Fafnir, Lesath, Maia, Meissa, Merope, Mimosa, Mintaka, Mira, Mizar, Nashira, Pleione, Polaris, Pollux, Porrima, Proxima, Ran, Rastaban, Rigel, Sarin, Shaula, Sirius, Sheratan, Situla, Spica, Talitha, Tania, Vega and Zosma
Dwarf planets: Ceres, Pluto, Haumea, Makemake, Eris, Salacia, Varuna, Orcus (who has his own moon named Vanth), Sedna
The moons of Jupiter: Io, Europa, Ganymede, and Callisto (which are the Galilean moons), Metis, Adrastea, Amalthea, Thebe (a different group called Amalthea group), Themisto and Carpo (two stand-alones), Leda, Himalia, Lysithea, Elara, Dia (of the Himalia group), but there are 67 total
The moons of Uranus: Miranda, Perdita, Margaret, Rosalind, Portia, Juliet, Mab, Desdemona, Cressida, Bianca, Ophelia, Cordelia, Titania, Oberon, Puck, Caliban, Sycorax, Prospero, Setebos, Stephano, Trinculo, Francisco, Ferdinand, Ariel, Umbriel, Belinda
The moons of Neptune: Triton, Proteus, Larissa, Galatea, Despina, Thalassa, Halimede, Sao, Laomedeia, Psamanthe and Neso, all the names of water deities, plus Naiad and Nereid, which are terms for water deities
The moons of Pluto: Hydra, Charon, Nix, Styx, and Kerberos
The moons of Mars: Phobos and Deimos (I wouldn't recommend these, as they mean "fear" and "dread")
The moons of Saturn: (62 total, 53 with formal names, not including hundreds of moonlets) The usable names include Titan, Rhea, Dione, Pan, Atlas, Pandora, Phoebe, Hyperion, Helene, Calypso, Albiorix, Thethys, Anthe, Pallene, Aegaeon (Aegean/Aegeon would work better, I think), Janus, Telesto, Kari, Fenrir, Aegir, Hati
Constellations: Andromeda, Antlia, Aries, Auriga, Caelum, Carina, Cassiopeia, Columba, Corvus, Cygnus, Draco, Gemini, Leo, Libra, Lynx, Lyra, Norma, Orion, Perseus, Phoenix, Pyxis, Sagitta and Vela, but see the full list here.
Called minor planets, there are way too many to list (488,449 and about 20k of them are named) so this will not be a complete list - instead, I'll only show the names that are rare and could arguably be used today. As you'll see, what is left is a pretty fascinating list. You can find a full list of asteroids here. Did you know asteroids can have their own moons?
Female: Leda, Polyxena, Svea, Libera, Wilhelmina, Maximiliana, Agnes, Briseis, Ilse, Pelagia, Ilona, Egeria, Lenka, Beryl, Caecilia, Cordelia, Desiderata, Alauda, Enid, Okyroe, Hermione, Hebe, Ida, Acacia, Guinevere, Gunila, Coralina, Adelinda, Vesta, Dulcinea, Pamina, Pandora, Adrastea, Adria, Belisana, Lucina, Pomona, Lucretia, Tigerlily, Kallisto, Cornelia, Anahita, Beatrix, Ianthe, Ekaterina, Galilea, Galina, Embla, Bettina, Antonella, Wanda, Elba, Eliane, Cybele, Oenone, Pallas, Juno, Iris, Fortuna, Thisbe, Ursula, Frostia, Gallia, Calpurnia, Thais, Calvinia, Camilla, Eugenia, Ismene, Davida, Honoria, Xanthe, Xanthippe, Xenia, Helga, Carelia, Albina, Hesperia, Sabine, Leocadia, Una, Undina, Roswitha, Hestia, Bellona, Helmi, Alisary, Cosette, Odessa, Flavia, Cosima, Gladys, Tigris, Nicandra, Niobe, Phaedra, Allegra, Altamira, Amalthea, Castalia & Kastalia, Petrina, Sandrine, Eugenia, Mera, Rhiannon, Nenetta, Ambrosia, Mahalia, Aemilia, Verenia, Alsatia, Lilium, Helina, Saskia, Amalia, Ginevra, Genoveva, Octavia, Nerina, Amadora, Persephone, Brixia, Tanith, Sirona, Mimosa, Ghislaine, Ida, Salix, Imelda, Valina, Laetita, Ashpatra, Oriola, Ludmilla, Lobelia, Ampella, Iva, Titania, Nephele, Aspasia, Aegina, Melusina, Atira, Aralia, Arcadia, Ulla, Alisary, Kalina, Leukothea, Kalliope, Avila, Azzurra, Brianza, Pippa, Imogene, Solene, Iphigenia, Hermia, Bondia, Raimonda, Illyria, Toscana, Sybil, Olga, Brunsia, Peregrina, Blythe, Tirion, Vanadis, Eulalia, Kira, Caia, Calandra, Zelima, Olympia, Tirza, Raphaela, Chryseis, Gismonda, Mimi, Sequoia, Mira, Tove, Zita, Winifred, Coppelia, Maeva, Magdalena, Celestia, Cesarina, Feronia, Misa, Frieda, Cloelia, Lyka, Crescentia, Salome, Ursa, Ursina, Larissa, Lilith, Priska, Prisma, Chandra, Tomyris, Lunaria, Chantal, Malva, Malvina, Signe, Charis, Marceline, Ostara, Cybele, Cyrene, Saga, Deidre, Minerva, Romilda, Thora, Thyra, Petunia, Concordia, Lorcia, Dagmar, Davida, Tamsin, Millarca, Fabiola, Moira, Phryne, Doronina, Thisbe, Delphine, Demitra, Edda, Eudora, Fennia (Latin for Finland), Salvia, Galatea, Galene, Marcelle, Otila, Ottilia, Lagia, Wendeline, Fey & Fay, Klio, Sigrid, Franzia, Isolda, Jetta, Zenobia, Katja, Palatia, Kalypso, Lioba, Luce, Proserpina, Leonora, Stana, Musa, Polina, Lysistrata, Oceana, Marion, Malala, Tarsila, Nausikaa, Nortia, Ophelia, Praxedis, Raissa, Rosalinde, Zibeline, Rosamunde, Scheherezade, Zelia, Sebastiana, Valeska, Yvette, Yvonne
Male: Osiris, Salazar, Duncan, Zephyr, Xanthus, Wilbur, Rubin, Valentine, Seneca, Jurgen, Iskander, Alcide, Leonidas, Mingus, Eros, Jarvis, Hektor, Ixion, Escher, Troilus, Ulysses, Sylvester, Irvine, Carlisle, Skip, Fitzroy, Merlin, Anubis, Ninian, Cadmus, Midas, Davy, Eos, Kendrick, Dante, Sanford, Aramis, Rufus, Selwyn, Ajax, Sheldon, Bede, Odysseus, Bardwell, Varuna, Moa, Orcus, Thersander, Ignatius, Nestor, Siegfried, Sigmund, Cicero, Milton, Icarus, Slade, Acer, Mikko, Stetson, Girard, Lothar, Silvain, Eros, Lazzaro, Icarus, Wallace, Roderick, Pyramus, Kieffer, Fabian, Seeley, Morvan, Tremaine, Joris, Amos, Morris, Endymion, Preston, Bowen, Melchior, Bastian, Caspar, Miller, Castander, Callander, Miro, Romero, Gawain, Lucidor, Merrick, Joëloïc, Pascal, Kent, Fletcher, Chesley, Grover, Clasien, Fauvel, Miller, Cyrus, Cyrano, Drago, Ferris, Priamus, Luderic, Howard, Heath, Jessop, Kato, Warren, Lowry, Laertes, Maynard, Nigel, Nikko, Orpheus, Pan, Picander, Quincy
Last, but not least, here are some famous astronomers:
Galileo Galilei, Nicolaus Copernicus, Johannes Kepler, Edwin Hubble, Tycho Brahe, Isaac Newton, Carl Sagan, Claudius Ptolemy, Azophi, Christiaan Huygens, Giovanni Cassini, Edmond Halley, Charles Messier, William and Caroline Herschel, Harlow Shapley, Henrietta Swann Leavitt, Frank Drake, William Hartmann, Lyudmila Karachkina, and Jocelyn Bell