A. Most of them are simply names I like -- names I think will sound good in a book.
Percy is short for Perseus, the old Greek hero. I know the original Perseus was the son of Zeus, but as explained in The Sea of Monsters, Percy's mom named him this because Perseus is one of the few heroes who has a happy ending (in most versions).
Jackson is a name I've always been fond of for many reasons. I was an American history teacher when I wrote the Lightning Thief, so I was teaching about Andrew Jackson and Stonewall Jackson. My grandfather's nickname was Jack. Also, Jackson was the name of my protagonist in the adult mystery series I began writing in 1997, which featured private eye Jackson "Tres" Navarre. I just thought it sounded good with Percy.
Annabeth is a name I made up. I've never known anyone named Annabeth, though I've met a few fans with that name since. Also, Annabeth is modeled after Atalanta, the most famous Greek heroine, who is also described as a blond warrior girl with fierce eyes.
Grover? I don't know. I guess I watched too much Sesame Street as a child.
Some names were picked as shout-outs to people I knew. Mrs. Dodds is based (loosely) on a real Mrs. Dodds who taught math at the school where I worked. Mr. Brunner was the Latin teacher there. Connor Stoll, Travis Stoll, and Charles Beckendorf are all former students of mine. I also had students named Miranda and Nico.
But like I said, most names I pick because they just work well. I also have to be careful not to have too many names with the same first letter. It would get confusing, for instance, if everyone's name started with 'S' -- Sam, Sean, Shaw, Sally, and Susan.