There are two main conventions for naming equal-tempered set classes.
One derives from Allen Forte, whose The Structure of Atonal Music (1973),
is one of the first works in musical set theory. Forte provided each

set class with a number of the form c-d, where c indicates the cardinality
of the set and d is the ordinal number. Thus the chromatic trichord {0, 1, 2}
belongs to set-class 3-1, indicating that it is the first three-note set class
in Forte's list. The augmented trichord {0, 4, 8}, receives the label 3-12,
which happens to be the last trichord in Forte's list.

Forte's nomenclature is a divisive issue in the music-theory community.
The primary criticisms of the system are the following: (1) Forte's labels
are arbitrary and difficult to memorize, and it is in practice often
easier simply to list an element of the set class; (2) Forte's system
assumes equal temperament and cannot easily be extended to include
diatonic sets, pitch sets (as opposed to pitch-class sets),
multisets or sets in other tuning systems; (3) Forte's original system
considers inversionally related sets to belong to the same set-class,
though there are some musical situations in which this is not desirable.