I was thinking along the lines that if the number of future fathers dying remains constant than the naming should remain constant too. Only if the number of death per day increases then the naming would increase too. But it’s just speculating as I don’t know what really happened :)

I don’t think so as each dot is the rate at that day.

Because casualtity rates were at more less constant level throughout those month. So if we assume that only those where the father was killed would be name after them then the rate of naming could stay somewhat constant too.