Sortable name or sort name is sometimes used.
"Sortable name" is to be the standard term used in Canvas LMS, a popular software application for managing schools, colleges and other educational institutions - for instance here's documentation from Rutgers U. Music/recording database MusicBrainz, one of the most common systems for tagging audio files, uses the similar term "sort name" (see this example record).
Some systems prefer name for collation, e.g. documentation for the Emacs Multimedia System. Collation is the process of sorting things, e.g. names, in alphabetical order. Note that "collation name" is often used in databases for the specific rules describing how text is sorted (i.e. the rules describing how sets of collation rules are named), so there is a risk of confusion.
Having said that, many systems only store names in the form "surname, forenames" or similar, as in the Library of Congress name authority file used for US libraries. So they just call it a "name" and don't have a distinct term for this format. FAST calls it a label; the French system IDRef calls it a "Point d'accès autorisé". You could use this along with "display name".