Conventionally the name of the note which is the root is used to denote the chord, thus a major chord built on C is a C Major chord. The analysis and theory of tonal music usually treats the roots as the defining feature of chords and much information can be gained from a progression of roots even if chord types are unknown. Also, if the key is known then the chord forms are known for each root.
Often the root is not actually the lowest pitch being played in a chord, in which case the chord is inverted.