There is no specific name for a fear of "bugs", but it can generally be classified as any of the following:
Entomophobia (or Insectophobia) - fear/dislike of insects (often used to refer to bugs in general)
Arachnophobia - fear/dislike of Spiders (and/or other arachnids such as scorpions, ticks, and mites)
Apiphobia - fear/dislike of bees
Mottephobia - fear/dislike of butterflies and/or moths
Yes there is and it's called Ball phobia
phobia of dogs
Metallophobia
entomophobia or insectophobia
Tree Phobia
PenisJacker
Stache-a-phobia
When a dog is afraid of lighting it is called a noise phobia.
The fear of bugs is called entomophobia. This can include the fear of bees, but not the fear of spiders, as spiders are not really bugs.
The fear of bugs is entomophobia, or alternately insectophobia.
Hibernophobia
Atychiphobia, the fear of failure.