I understand that, but what I'm saying is that if the number of fathers dying remains constant than the naming will gradually increase for 9 months at which point it will remain constant. If there's 100000 fathers and 1000 died a week and there is also 1000 births we would only expect 1% or 10 of those babies to have dead fathers. This means that the number of babies with dead fathers is proportional to the proportion of fathers who are dead. The next week if both numbers remained constant we would expect the number to be 2% and so on. Conversely even if fathers stopped dying there would still be a large number of births with dead fathers for several months.

I'm not sure what you mean I understand that each dot is the rate at that day. My point is that if all the fathers died at once we would expect the naming chang to instantly rise and stay high as it is here for roughly 9 months. This is because the child isn't named when the father dies they are named when they are born some time in the next 9 months.

I understand that, its just odd to me that everyone went to max concern in just one week. I would have thought as the war went on and more soldiers died the rate of naming would increase. Especially considering it only rises roughly 5 percent. Remember in that first data point is late July to early August which actually means that the bloodbaths of August and September had little effect

I would disagree since there are two things that need to happen based on that assumption. The father has to die, and then the baby must be born. If the fathers deaths follow a perfect step function (i.e they are constant once war is declared) the rate of naming will increase as the proportion of dead fathers increases. Based on that assumption what this data implies is almost all of the fathers died simultaneously. Basically the rate of naming is the integral of the rate of deaths

While its not surprising to see an immediate increase, it is strange that it would increase so sharply and then stop. As you say over the few months after the war began the casualties increased significantly so you would expect the rise here to increase constantly over those months to some degree. There was certainly space for it to do so as the percentage never really maxes out (I would say the max is below 100% given many family's will already have sons named after the father but still). There could have been some national push towards naming children for there fathers over one specific week but I think its more likely that there is some irregularity in how the data was collected which seems likely in war time.

Even if there was an immediate increase, I can't see why that increase wouldn't continue as the war got worse throughout the year.

But the confusing thing is the jump stayed at 5%. I can see there being an immediate uptick but I'd expect that rise to continue for a while before leveling.