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.
I found a fatwa in Arabic, where a man found out that he was adopted and he inherited from his adoptive father and the family of his wife wanted to declare his marriage as invalid as they felt cheated because his family name was false. This is briefly the basis of the fatwa question.
The answer about the marriage was: the nikah is valid but he must change or better correct his name and the family documents because of these ahadith (for example) from sahih Muslim and sahih al-Bukhari and the Verses (33:37-40) and (33:5) see also the explanation of these Verses in sunan at-Tirmidhi or in sunan an-Nasa-i.
So the marriage of your mother is valid, but she has to change her family name and documents for her peace of mind!
And Allah knows best!