Claiming

The act of being claimed occurs when a god acknowledges his/her demigod offspring, usually by sending a hologram of their symbol of power to appear over the particular child's head, but some claimings are unique, such as Piper's when her makeup, hair and clothes are changed to enhance her beauty.

Children of minor gods did not have their own cabins at Camp Half-Blood, so they were sent to live in Hermes' cabin once claimed and were probably only given small recognition due to their parent's minor status. However, as part of Percy's request to the gods, cabins are made for all of the children of the gods, as part of Luke Castellan's dying wish.

Some campers were never claimed, so they also stayed in the Hermes cabin along with the minor gods' children and the children of Hermes. This is also remedied by Percy and now all gods are required to claim their children by age 13.

Poseidon's Claiming
When Poseidon claims one of his demigod or Cyclops children, a green trident hologram appears over their head. This happened to Percy after he healed his Hellhound wounds when Annabeth (realizing his capabilities) orders him into the creek so Chiron could view his powers, Poseidon claims him while everyone bows. It later happened to Tyson in The Sea of Monsters after he enters Camp Half-Blood while he stood waiting in the dining pavilion of the Big House as he was being taunted by Tantalus, the substitute activities director for Chiron, while Tantalus was taunting about his Olympian godly parentage.

Aphrodite's Claiming
When Aphrodite claims her children they start glowing with a pink aura. After that they instantly look great (beautiful). The children of Aphrodite refer to this as Aphrodite's Blessing, which goes on for a while and can sometimes even go back when Aphrodite wills it to, but may fade after a while. This happened to Piper while she was at the camp's bonfire in The Lost Hero.

Hephaestus' Claiming
When Hephaestus claims his demigod children, a red fiery hammer appears over their head. This happened to Leo instantly after he arrived at camp in The Lost Hero.

During The Original Series

 * Percy Jackson - (The Lightning Thief)
 * Tyson - (The Sea of Monsters)

Greek Demigods

 * Annabeth Chase
 * Malcolm
 * Thalia Grace
 * Luke Castellan
 * Nico di Angelo
 * Connor Stoll
 * Travis Stoll
 * Silena Beauregard
 * Clarisse La Rue
 * Chris Rodriguez
 * Ethan Nakamura
 * Butch
 * Katie Gardner
 * Miranda Gardiner
 * Lacy
 * Drew
 * Mitchell
 * Harley
 * Nyssa
 * Charles Beckendorf
 * Christopher
 * Pollux
 * Castor
 * Shane
 * Mark
 * Sherman
 * Jake Mason
 * Austin
 * Kayla
 * Lee Fletcher
 * Michael Yew
 * Will Solace
 * Clovis
 * Lou Ellen

Roman Demigods

 * Hazel Levesque - (The Son Of Neptune)
 * Jason Grace - (The Lost Hero)
 * Reyna -(The Son Of Neptune)

During The Second series

 * Piper McLean - (The Lost Hero) (Greek)
 * Leo Valdez - (The Lost Hero) (Greek)
 * Frank Zhang-(The Son Of Neptune) (Roman)

Trivia

 * As shown in The Sea of Monsters, monsters like Tyson can also be claimed by their godly parent, even though they aren't considered demigods.