I found a nice article about the evolution of the IUS in this issue of the Crosslink newsletter.
Originally, NASA intended to develop a reusable "space tug" that could deliver satellites from the relatively low orbits reachable by STS to geosynchronous and other high orbits. This was a big concept that was going to take years to develop, so NASA and DOD agreed to develop an expendable Interim Upper Stage, IUS, to perform those sorts of satellite deployments.
As the article describes:
At the end of 1977, NASA abandoned its plans for a space tug, so the IUS program name was formally changed from Interim Upper Stage to Inertial Upper Stage (because it used inertial navigation). The prime contractor was selected, and full-scale development began in April 1978.
Obviously a desire to retain the established TLA informed the choice of name; it's not unique in using inertial navigation. It's a pretty poor choice of name all around; it's two stages, not one.