I don’t know many of the “whatever happened to …” stories but I’d assume, unless the character is from the future, there aren’t many Legionnaire names that would work. Rokk probably isn’t a common name in this century.
The child's name is one letter off from the Legionnaire, but phonetically the same. There's also a reference to the Legionnaire's super-hero name in the scene.
This is a character whose stories are generally considered to be set on Earth-One, though his first appearance was in an anthology that also contains stories of members of the Justice Society.
With that last name, it has to be the western Johnny Thunder, whose real last name was Tane. As should be obvious, I did not know that he was featured in one of those stories.
It is John Tane, mild-mannered schoolteacher of the old West, who adopts the dynamic identity of Johnny Thunder!
In DCCP #28, he teams up with and marries Madame .44, and they have two children, including Charles "Chuck' Tane, which, even if it weren't made pretty blatant by the emphasis on "bouncing" and "boy" in the panel, has been confirmed by the writer as a reference to the Legionnaire.