What is the name of the instrument for drawing blood for laboratory tests?

The needle is the same as the one we use for IVs, except that its other end (the one that doesn't stick you) is also sharp, but it pierces the rubber tip of the test tube. The test tube is vacuumed inside, and because of the pressure difference, the blood naturally stays in the test tube automatically.

It's just a needle and tube.

There are many kinds of test tubes, including dry tubes and anticoagulant tubes, and the cheapest ones cost a little more than a dollar. Needles are cheaper, I forget how much. You can buy them at a pharmaceutical company, but you can't buy them for individuals, they are only available to medical institutions and the like.