I suspect that this man enlisted as CLARKSON, and so is "mis-filed" in the WW1 Service Records (WO 363):

William Alexander CLARKSON, enlisted March 1915, declared age 19y, born Kingston, Surrey.
Home address: Kingston Hill
Father: Robert Harold.
Served with the RAMC, Regt Nos 3375 & 88874.
De-mobbed 1919.

There is only ONE Clarkson birth in Kingston (1893-1899) - a William HENRY. This could possibly be him.
There are FIVE William Alexander births (1893-1899), one of whom is William Alexander C CLARKE (Q3 1897).

If anyone can determine his proper name, please let me know so that the heading can be changed.

Anc****y, CLA, pages 194306-194320