We venerate the name of Mary because it belongs to her who is the Mother of God, the holiest of creatures, the Queen of heaven and earth, the Mother of Mercy. The object of the feast is the Holy Virgin bearing the name of Mirjam (Mary); the feast commemorates all the privileges given to Mary by God and all the graces we have received through her intercession and mediation. It was instituted in 1513 at Cuenca in Spain, and assigned with proper Office to 15 Sept., the octave day of Mary’s Nativity. After the reform of the Breviary by St. Pius V, by a Decree of Sixtus V (16 Jan., 1587), it was transferred to 17 Sept. In 1622 it was extended to the Archdiocese of Toledo by Gregory XV. After 1625 the Congregation of Rites hesitated for a while before authorizing its further spread (cf. the seven decrees “Analecta Juris Pontificii”, LVIII, decr. 716 sqq.) But it was celebrated by the Spanish Trinitarians in 1640 (Ordo Hispan., 1640). on 15 Nov., 1658, the feast was granted to the Oratory of Cardinal Berulle under the title: Solemnitas Gloriosae Virginis, dupl. cum. oct., 17 Sept. Bearing the original title, SS. Nominis B.M.V., it was granted to all Spain and the Kingdom of Naples on 26 Jan., 1671. After the siege of Vienna and the glorious victory of Sobieskl over the Turks (12 Sept., 1683), the feast was extended to the universal Church by Innocent XI, and assigned to the Sunday after the Nativity of Mary by a Decree of 25 Nov., 1683 (duplex majus); it was granted to Austria as d. 2. classis on 1 Aug., 1654. According to a Decree of 8 July, 1908, whenever this feast cannot be celebrated on its proper Sunday on account of the occurence of some feast of a higher rank, it must be kept on 12 Sept., the day on which the victory of Sobieski is commemorated in the Roman Martyrology. The Calendar of the Nuns of Perpetual Adoration, O.S.B., in France, of the year 1827, has the feast with a special Office on 25 Sept. The feast of the Holy Name of Mary, is the patronal feast of the Clerics Regular of the Pious Schools (Piarists) and of the Society of Mary (Marianists), in both cases with a proper office. In 1666 the Discalced Carmelites received the faculty to recite the Office of the Name of Mary four times a year (duplex). At Rome one of the twin churches at the Forum Trajani is dedicated to the Name of Mary. In the Ambrosian Calendar of Milan the feast of the Holy Name of Mary is assigned to 11 September.
(The above from New Advent.org)