It was ruled "natural causes" so there probably wasn't a need to go beyond that at the time of the autopsy. As far as I know they don't routinely test for cyanide, unless things have changed over the years. There would be no reason unless he was showing specific signs of poisoning. Just from a legal standpoint, the next in line for the money would need to at least be questioned since it happened so soon after winning.
Remaining anonymous depends on the rules of each individual state. But I do think they should all permit it.