Probably the most common reason in all countries was, underage enlistment, to prevent their parents having them removed from the forces, so what was his stated age when he enlisted, and was that his real age. ?
Some people also enlisted and then deserted and rejoined under a false name, but he seems to have enlisted under a false name and then, presumably after his discharge, reenlisted in his real surname.
In a smaller number of cases people might have been wanted by the law, or didn't want their spouse to know where they were.
In 1919 his wife seems to have been aware of his first, WW1, enlistment under a false identity, but did she know about that before they married in August 1919. ?
Perhaps she only found out about that after he returned to Australia in May 1918 and they were married in his real surname in August 1919, and presumably they married in Australia.
However, under the false surname in which he enlisted and served overseas for some reason until May 1918, he was making allotments to two different women, neither of whom was his future wife.
I wonder if whilst overseas in WW1, he might have married under his false surname, and then married bigamously when he returned to Australia. ?
Because for some reason his deception came to the attention of the Australian military authorities and apparently to the Australian military authorities in England, so how did that matter first come to their attention, by a complaint or an inquiry from one of the women perhaps. ?