I can't give you when it happened, but I can say that 2500 years ago in Ancient Rome it was the norm for children to refer to their parents via their title rather than their name. For example, in Menaechmi by Plautus, an early Roman Comic playwright, one of the characters repeatedly refers to her father as "father", and never by his name (he is in fact unnamed in the play).

MAT: salve multum, mi pater.

Greetings, my father.

and slightly later

MAT: Qui ego istuc, mi pater, cavere possum?

How, my father, can I possibly guard against that?

So the practice is very old. Perhaps a linguist could tell us if this form of address is the norm in Indo-European languages.

I would suggest asking AskAnthropology since humans have had names for kinship bonds for a very long time, before written history for sure.