That "Gregorian" chant was named for and credited to Pope Gregory I (r. 590-604) is an accident of politics and spin doctoring. Tension between the Pope (the Bishop of Rome) and other Bishops regarding the authority of the Pope as "first among equals" was matched by tension between the Pope, as spiritual ruler of Rome, and Rome's secular rulers. This tension was an off and on thing until as late as the 15th century, when the "Conciliar Conflict" (c. 1409-1460) pitted the power of the Council of Bishops against the power of the Pope and Cardinals.
Gregory I has been credited with many things, including the writing, collecting, or organizing of the body of plainchant in use at the time, as well founding the first singing school (Schola Cantorum) in Rome to train singers for the church, organizing the church's annual cycle of liturgical readings, and first establishing the church's authority over the secular rulers of Rome.
There are any number of lovely stories and legends associated with Gregory. There are paintings showing a bird singing chants into his ear as he wrote them down. (Unfortunately, of course, there was no usable music notation at the time.) There are stories of his sending out missionaries with instructions to bring back any new music they encountered, saying "Why should the Devil have all the good songs?"
Whether he actually did any of these things is questionable. They were attributed to him in later centuries in an attempt to build up and support the primacy of the papacy. Those who attributed wondrous accomplishments to Gregory were doing the same job that spin doctors do today for politicians and entertainers.
In point of fact, the chant that was used in Gregory's time is now known as Old Roman, which barely survived into the era of musical notation, passing from one generation to the next by ear. In about the year 800, two centuries after Gregory's time, the Emperor Charlemagne sent to Rome for authentic liturgical books and chants. Singing teachers were dispatched from Rome to teach the Franks by ear, but they did not get along well and the Franks made major changes in order to adapt the chant to their taste and their ways of singing.
The chant of the Franks is the style that eventually propagated. As a result, what we call Gregorian chant should probably be called Carolingian chant, but the easy way out is simply to use the term plainchant and leave it at that.
John Howell