The index finger is between your thumb and middle finger.

There is no scientific name for the width of the index finger. The name index finger literally means pointing finger.

It goes on the index finger because the index finger is the only finger that has a tendon connected to the heartThere is no scientific name for the width of the index finger

is the index finger lateral to the ring fingers

An INDEX is defined as a "pointer" - from Latin: informer - that which points. It is the finger used for pointing, thus the "index" finger.