The title everyone uses for Gabriel is not in the books he appears in. It was given to him later, and following who gave it is a short lesson in how a tradition builds ranks for its unseen beings.
What the texts say
The New Testament uses the word archangel twice, and neither time of Gabriel. The letter of Jude names Michael the archangel, and 1 Thessalonians mentions the voice of an archangel without a name. Daniel calls Gabriel a man in appearance. The rank is an inference, and a reasonable one, but an inference.
Where the rank comes from
The Jewish apocalyptic literature of the Second Temple period supplies it. 1 Enoch lists a small group of chief angels standing before the throne, Gabriel among them, and later Jewish and Christian writers settle on four or on seven, with Michael, Gabriel, Raphael and Uriel the names that recur. Rabbinic and later mystical literature keeps Gabriel in that company.
The name
Gavriel in Hebrew is read as God is my strength, from the root for strength or a strong man together with the divine name El. The reading is old and is not seriously contested.
Feasts
The Roman calendar kept a separate feast of Gabriel on 24 March, the day before the Annunciation, until the revision of 1969 joined Michael, Gabriel and Raphael in one celebration on 29 September. Eastern Christian practice commemorates the bodiless powers together on 8 November and keeps its own commemorations of Gabriel besides.