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6.5.3 Chord Root: How to Name a Chord
A chord is named for its chord root, and chord progressions (harmonic intervals) are named according to the intervals between chord roots.
Melodic intervals, by contrast, have logical, straightforward names (more or less). A perfect fourth is the interval between the tonic note and the fourth note of the diatonic scale. A perfect fifth is the interval between the tonic note and the fifth note of the diatonic scale.
Naming harmonic intervals (chords) is not so straightforward. Chord movements (progressions) are named for the intervals between chord roots, even though the term "chord root movement" has no intrinsic meaning.
It’s the whole chord that moves, regardless of root or inversion. The chord "C major" keeps the name "C major," regardless of whether it's in root position, first inversion, or second inversion.