Is nikah valid when one is called by his step father's name?

My Mom and Dad has been in Nikah for more than 20 years, and my mother has been called with her step father's name since. I recently got to know from a drama serial that Nikah is not valid if spouse(s) is/are called with their step father's name, but I want to confirm if this ruling is true. Prescribe in the light of Koran and hadith. As soon as I come to know, I can persuade my parents to perform Nikah again or not.