Hi,
As mentioned above it was quite a common occurrence for stepchildren to take on the stepfather's name.
My hubby's g grandfather's two stepchildren took on his surname ( this was in the late 1800's) . The stepdaughter even used her stepfather's surname when she married, she also listed her stepfather as her father in the church records, so if anyone traced her lineage by her marriage certificate only, they would get the wrong man for her real father.
The two stepchildren were old enough when their real father died to remember him, so it was definitely a conscious decision to use their stepfather's name.
The stepdaughter also named her own children's Christian names after their stepfather.
My guess is: he was just like a real father to them, so they took his name. They were quite a large close a knit family
Kind Regards:)