You don't specify exactly when these children were born, but there are two scenarios, both of which were known to happen. One is that Gerson was widowed and then married his wife's sister. Who would be a safer step-mother than the child's aunt? The other scenario is that various names appeared on the children's birth and marriage records for the same mother.
My 3-greats-grandmother was Sophie Schiren, daughter of Simon Schiren (Schieren on other records), on her 1809 marriage record in the Rhineland. On her children's birth records, she was Heba Schirot (1810), Eve Simon (1812), Hebbeken Simon (1814), Eva Simons(1816), Heva Scherath(1819), Heva Schierath (1821), Eva Schierath (1823), Eva Schiratz(1826).
Her death record (1857) says Sophie, but her grave says העווה (an alternative spelling of Chava/Eve), and within a few years four grandchildren were named Eva. None of her grandchildren were called Sophie.
Generally, the same mother's name appeared on the child's birth and marriage record, but there was not much consistency between children - it was never exactly the same.
I have another example, from the Moselle region of France - my 5-greats-grandfather's 2nd marriage was to Sara Franck, the widow of Abraham Bondy. 5-greats-grandpa had five children with Sara, but on the birth record of the fourth, the mother is named as Schwartzle Bontay. Schwartzle has to be a nickname, and Bontay a reference to her first husband, but it confused the person who documented the town to the extent that he treated my 5-greats-grandpa as two people.
So, my suggestion would be to look for evidence of the death of a first wife, or marriage records to prove that there were two wives. If you find no such evidence, then it is reasonable to assume multiple names for the wife. In the ideal world, you will find the marriage record and death record of the wife which establish that it is the same wife from first child to last, despite any name variations.
I hope this helps,