Good work Monica

If like me, I get confused with info. giving married surnames then (born x) as it's so much easier working with maiden names from start off.
Anyway...
all births in Wolverhampton up to 1920 showing as Adamson, with mother's maiden name Britton.
Do you have an occupation for J C Adamson?
It may be an idea to get the
last birth (1920) for an occupation.
Another thought is whether "D N Adamson and Robina Patterson (otherwise adamson)" were husband & wife or brother & sister?
Looking for a marriage for D N Adamson may give a father's name or finding him on 1911 may help with POB (Place of birth)?
I couldn't locate J C in 1911 either but haven't looked for D N Adamson.
Could find neither on
any census' in Scotland from 1881

I couldn't find a birth for J C or D N Adamson in Scotland i.e. may have been illegitimate but took on their father's surname which wasn't unusual?
Does J C's enlistment not give a NOK (Next of Kin) which may name his mother & an address?No father named on marriage may be an indicator he didn't know his father's name?
Edited as I note he was already married when he enlisted

Annie