Do you think the eye will gain a name? If Boruto and Sarada somehow have a child, would it evolve into something entirely different? Why only one eye?
Personally I think the eye should be called Getsugan because it looks like a moon in the sky. -edit apparently kishimoto said that if a sharingan user and byakugan were to have a child, the eyes would be split. chances are, the kid would have either boruto's dojutsu in one eye and a sharingan in the other or the mutation would fade away into a byakugan. there are chances of two distinct lines with sharingan or the new dojutsu. just look at hagoromo and hamura and then hagoromo's kids asura and indra