Eileen B SCOTT appears in the 1939 Register living with her grandmother Jessie Maud SCOTT. It is not clear whether she had reverted to the name SCOTT or whether the enumerator thought 'BROWN' to be a middle name.
No married name was later added to the 1939 Register, so it is likely that she never married. That said, there are several Eileen BROWNs that married after the Second World War in Liverpool, the best fit is the Eileen BROWN that married John J NEWALL in Q2 1950. An Eileen NEWALL, born 1922, died in Q2 1957 in Liverpool North. No civil births for that couple were registered.