Originally, "Mizuko" was pronounced as 'suiji,' and it was one of the Igo (names according to age and sex) which was placed after the posthumous Buddhist name, given in case of stillbirth or given to those who died prematurely.
“水子”は本来「すいじ」と読み、戒名の下に付ける位号の一つで、死産や乳児の頃に夭折した者に対して付けられるものであった。