Here's a story that initially appeared in one of my social media feeds. Suffice it to say, I found the story so odd, that at first I was tempted to write it off as a hoax. However, it does turn out that there is some actual evidence of personality variations among cockroaches. The basic categorization seems to be one of "shy or cautious" versus "bold explorers". The explanation currently is that individual personality variations in cockroaches enable the species to survive when disasters occur. The belief is that at least a few of the creatures survive, depending on the circumstances surrounding the disaster, thus enabling those survivors to continue to propagate.
This is not the first time that I have seen mention of cockroaches as somewhat more complex creatures than they might appear on the surface. A number of years ago, a social psychologist named Bob Zajonc conducted experimental research demonstrating that under some circumstances, cockroaches showed the same sorts of social facilitation effects found in humans. One could almost imagine a follow-up experiment in which the newly discovered personality traits would serve as a "person variable" that might interact with manipulations of social facilitation (the presence or absence of other cockroaches).