A nikah solemnised with the consent and permission of parents carries blessings. And morally a boy and girl should inform their parents about their nikah. However, in the question mentioned, if they (boy and girl) did their nikah in the presence of legal witnesses and no condition of nikah’s validity was missed, then the nikah was valid. And the intercourse that took place after nikah was lawful. Now, there is no need to do new nikah only to make your parents and people aware about your nikah, because if after the second nikah and before six months any child is born, people will get doubtful. Yes, if your wife is not conceived yet and there is nothing sort of doubt, then the nikah may be repeated.
Allah (Subhana Wa Ta’ala) knows Best
Darul Uloom Deoband