It is most likely that Pope Gregory wrote few (if any) of the chants. He decreed that all chants be codified in order to establish uniform usage. He also assigned certain chants to certain masses throughout the year as standard. His collecting and organizing of these chants (most of them anonymously written) is why the genre is referred to in his honor as "Gregorian." As most chants do not have a named composer it was most effective to label it thusly. This label (or the use of "Gregorian" as the official term) most likely began in the ninth century and Pope Leo IV.
Stolba, Marie K. The Development of Western Music The MacGraw-Hill Companies, Inc. 1998. Third Edition. P. 23