I think that they would be careful not to name too many of their kids directly after people who had prophesies and terrible fates, as they might suffer the same fate as those heroes. Instead, they would use similar names.
Percy and Annabeth
Charlie- 16
Lucas- 16
Serena-14
Zoey- 12
Bobby- 9
Hazel and Frank
Emma-13
Mason-11
James- 9
Jason and Piper
Jaycee- 20
Tris- 20
Leo and Calypso
Aiden- 15
Esther-13
Beck- 11
Sam- 9
Reyna and Nico
Bella- 18 (She's actually Hylla's daughter that they adopted.)
Hannah- 13
Maria- 11
Bianca- 11
Haden- 9
Julius- 7
Amelia- 4
Travis and Katie
Willow- 14
Marcus- 12
Johnathan- 10
Sadie and Walt
Angie- 15
Harper- 12
Warren- 9
Carter and Zia
Joseph- 15
Ruth- 13
Zachariah- 11
Tyler- 9