There are many studies that show the role of fasting and neurogenesis, specifically time delayed restricted eating versus pure calorie restriction. All of the studies I've seen so far are in mice.
However, the original question is whether neurogenesis leads to behavioral change. Neurogenesis for adults appears to largely happen in the hippocampus which is understood to be the center for learning and memories. This review examines other potential ways the hippocampus, and thus the neurogenesis caused by fasting, impacts behaviors.
Although it is uncertain how hippocampal roles in learning/memory and emotion are related, it is clear that an accurate picture of the function of new neurons in the hippocampus must account for all of their behavioral effects, including those with emotional but not mnemonic components. One potential role for the new neurons, and the rest of the hippocampus, that appears to fit with both emotional and memory-related findings is in predicting possible outcomes of novel or ambiguous events and in emotionally biasing these predictions.
Here they show in a few studies that mice with lesioned hippocampuses change their behavior when faced with new challenges like potential predators they hadn't interacted with before. This review hypothesizes that the hippocampus will bias future behaviors in new situations through emotional learnings.