Chord names are generated from a list of pitches. The functions which construct these names can be customised.
Here are shown chords following Ignatzek (pp. 17-18, 1995), used by default since LilyPond 1.7.20, compared with an alternative Jazz chord notation and Harald Banter's (1987) notation. A smaller font is used in the latter case, as these tend to be overly verbose.
This mirrors the mechanism originally used in early LilyPond versions (pre-1.7); not having been properly maintained, however, some features have been lost (mainly chord exception lists) and bugs have been introduced.