All names are taken from Greek Mythology
Move two names from Asphodel to Elysium
Move two names from Asphodel to Tartarus
Move one name from Elysium to Asphodel
Move one name from Tartarus to Asphodel
When all names are in Elysium of Tartarus, eliminate one you don't like from Elysium, and one you like from Tartarus until there is only one left in each.
Elysium:
Menelaus, Hector, Perseus
Fields of Asphodel:
Achelous, Achilles, Actaeon, Adonis, Aegeus, Aegisthus, Aeneas, Aeolus, Aethiolas, Ajax, Amphitryon, Antaeus, Antenor, Antinous, Antiphus, Apollo, Ares, Argus, Asclepius, Atlas, Boreas, Castor, Charon, Chiron, Ctesippus, Daedalus, Diomedes, Dionysus, Elatus, Ephialtes, Erebus, Eros, Eurus, Hades, Helenus, Helios, Hephaestus, Heracles, Hermes, Hippomenes, Hyllus, Hyperion, Iasus, Icarus, Iphicles, Janus, Jason, Kronos, Laertes, Lycaon, Maraphius, Megapenthes, Meleager, Mentor, Midas, Minos, Narcissus, Neoptolemus, Nereus, Nessus, Nicostratus, Notus, Oceanus, Odysseus, Oineus, Orion, Orestes, Orpheus, Otis, Ouranos, Parthenopaeus, Patroclus, Peleus, Perdix, Periphetes, Phaethon, Phoebus, Pleisthenes, Pollux, Polybotes, Polybus, Polydamas, Polyphemus, Poseidon, Priam, Procrustes, Prometheus, Pygmalion, Pyrrhus, Sciron, Sinis, Tantalus, Tartarus, Telemachus, Teucer, Theseus, Triton, Tyndareus, Zephyr, Zeus
Tartarus:
Agamemnon, Deiphobus, Paris
It's a lot easier to come up with 106 male names from Greek Mythology than female ones.