The name "Classical" was coined by me to reflect the fact that the near-circular orbits of these bodies are, amongst the known KBOs, the closest to expectations from dynamical models existing when the Kuiper belt was discovered. These models predicted that the Kuiper belt would be thin (it is very thick) and the orbits of KBOs would be nearly circular (most are highly elliptical). The "Classical" label means that these objects are the closest to this 'classical' expectation.
The first example of a Classical KBO was the first recognised KBO: 1992 QB1.
An alternate name, "Cubewanos", was proposed as a play on the name of 1992 QB1 (provided you pronounce QB1 as cue - bee - wan, not cue - bee - wun).