My father's father's ánd father's mother's families did the same as Mailyn's.
My great grandfather Joseph Servian (Josiel SerwianskI) had three children who came with him to Liverpool in c 1875. One of those children born Baruch Serwianski used the names Barnett Servian, then Barnet Silverman and then when he emigrated again to USA in 1905, he called himself Barnet or Bernard Maxwell - after Joseph's father Mordecai. Joseph's daughter Leah died young of typhoid aged 16 in North Wales, and she was buried as Leah Max (again after Mordecai).
My other paternal great grandfather Nathan Abrahams (born Chackiel or Casper Ceglarski) reverted to the family patronym when they came to Manchester in 1867. Both his father and son were called Abraham Abrahams or Abrams.
The Servians came from Sejny and the Abrahams came from Suwalki both in Suwalki gubernia.
Jill Whitehead, Surrey, UK