Most demigods' last names seem to relate to their Olympian parent:
1.Silena Beauregard, daughter of Aphrodite - Beauregard is French. It literally means "good looking".
2.Lee Fletcher, son of Apollo - A fletcher is someone who makes archery arrows.
3.Micheal Yew, son of Apollo - Yew is a favorable choice of wood to use for longbows.
4.Nico di Angelo, son of Hades - Nico is most likely deprived from the prefix Necro, to mean "dead". Di Angelo means "of angels".
5.Will Solace, son of Apollo - Though Solace really means "to comfort in distress", just as Will comforted and healed Annabeth when she was injured, Solace could also be a play on the word "Solar".
6.Thalia Grace, daughter of Zeus - The name of one of the three Graces (and nine Muses) is Thalia. She too, was a daughter of Zeus. The Muse Thalia sired the Corybantes, with Apollo. This Thalia was also attracted to Apollo.
7.Pollux & Castor, twin sons of Dionysus - They share the same names as the twins of the Gemini.
8.Jake Mason, son of Hephaestus - Mason means "one who works with stone".
9.Clarisse La Rue, daughter of Ares - La Rue is french, and means "Street". Which doesn't entirely relate to anything about Ares. However, rue is to regret, as Clarisse inflicts regret to all who face her in battle.
10.Travis and Connor Stoll, sons of Hermes - Their name is a homonym for stole, as Hermes is the god of thieves, which was brought up in the Sea of Monsters.
11.Katie Gardner, daughter of Demeter - Demeter is the goddess of the harvest and her last name refers to one who gardens or works with plants.
12.Miranda Gardiner, daughter of Demeter - Demeter is the goddess of the harvest and her last name refers to one who gardens or works with plants.