As I understand it, he enlisted aged 17½ in 1906 under the name of Matthew Hedges, but was in the 1911 census and married that year under the name of Alfred Mays, so the name change came between then.
Two theories:
1. Something happened in the army causing him to leave one regiment and rejoin another under a different name.
2. He changed his name in order to inherit money when he reached 21. I have a relative who did this, but only added a surname,
he didn't change his first name as well.
The fact that he kept his given names as middle names make me think that he didn't do anything illegal.
I dont know, Margp as I've never come across it before. As you order certificates by the number I wonder what they would send you?