[Back ]That is the "popular version".
"The Venerable Bede" (c. 673-735, historian-monk of the north of England), instead, quotes the exchange as follows in his work "Historia Ecclesiastica Gentis Anglorum":
Responsum est, quod Angli vocarentur. At ille: "Bene," inquit; "nam et angelicam habent faciem, et tales angelorum in caelis decet esse coherides."
He was told they were called Angles. "It is well," said he, "for they have the faces of angels, and such must be co-heirs with the angels of heaven."