Was the insect named for the annoyance or the annoyance for the insect? I didn’t know so, of course, I went to Wikipedia.
A bug is an insect of the order Hemiptera, known as the "true bugs”.
Clear as mud. I went searching for more information. Using Google I found an article on SFGate.
It is from an old Welsh word, bwg (pronounced boog), which means evil spirit or hobgoblin and may also be the origin of the boogeyman, the imaginary creature that haunts little children.
So there you have it. Maybe.