Why is Microgravity called "Microgravity"?

Microgravity is used because zero gravity is inaccurate. The ISS, at 400 km, experiences an average atmospheric density of 4 nanograms per cubic meter. It's frontal area varies from 700-2300 square meters. At 1000 m$^2$, the drag force is $ \frac 1 4$N. With a mass around 250,000 kg, that's $10^{-6}$ m/s$^2$, or 0.1 $\mu$g.

Hence: microgravity, literally.

If you leave an object at the back of the space station, it will fall forward, falling 100 m (the length scale of ISS) in 4 hours, with an impact speed of $\sqrt 2$ cm/s.

Microgravity doesn't mean that the gravitational field is negligible, just that the system in question does not feel its effects due to being in free-fall. The interior of a freely-falling elevator is a microgravity environment - at least until it hits the ground.

You are not the only person who has problems with the term microgravity. I doubt there is any record of how or why the term was coined.

My guess is that NASA introduced the term microgravity because it sounds more scientific that "zero gravity" (which is just plain wrong) but less scary than "free fall", which is accurate but might suggest to the man in the street the ISS was about to fall out of the sky.

This article suggests that due to active stabilisation the environment on the ISS is actually closer to "nanogravity" than microgravity.