What is the name of this biting bug?
It's a larva of a green lacewing (Family Chrysopidae). Yes, they can bite hard but you're not its intended victim and they're not only harmless but beneficial as they're aggressive predators of aphids and other soft bodied plant pests. I can't be specific to what species of lacewing as they look fairly similar.

Another larva that looks very similar to yours.


Source from BugGuide.net

What the adult looks like (remember,they're an entire insect family so there are differences but not to most people).


Source also from BugGuide.net