Originally Posted by
Korath
Why ? He isn't Kryptonian, he's an Earthling, and a US citizen to be more precise. His ties to Krypton's culture are even weaker than his father's. It wouldn't make a lot of sense for him to have one. He is the Son of Superman and Lois Lane but the only world he knows as a child his Earth, and its cultures.
I know that some peoples want their children to have names from other cultures than the main one in the country they live in, but usually, it's because they have a deep-rooted attachment to their place of birth (or for religious reasons, obviously). But in Clark's case, krypton always felt so remote that it'd be strange that he want to name his only child with a Kryptonian name. Plus, it would have been a secret name since until he revealed his identity, Jon couldn't have been using it anyway.
That's why (Hyppo)Lyta makes sense for the name of a Wonder Woman's daughter - she loves Themyscira and she has deep rooted cultural and familial ties to it. Naming a children after her mother makes sense in that regard.
With Jon, it'd feel cheap, I think.