When I found the Irish marriage and subsequent births, I had an idea that Owen and Eugene may be the same child.
William Moran is listed as being 12 years old on the 1901 census in Strathaven.
According to the Military papers, William Morran was born in Strathaven and was 19 yrs and 1 month when he first signed up ( RH and RFA) on 24 Jul 1907 and was discharged 23 Jul 1919 .
He spent most of his early career in India before being sent to France.
William was awarded the Military Medal in 1917
His mother Jessie, brothers John and Thomas lived at: 14 Earston Ave, Glasgow
He married Lizzie Taylor in Glasgow 1 Jul 1918
Edit:
William's wife lived at: 12 Cobden St, Calton, Glasgow