Currently the Roman Rite of the Catholic Church honors the Holy Name of Mary with an optional memorial on September 12.
The feast is closely associated with the birth of the Virgin Mary, which is celebrated on September 8.
According to the Catholic Encyclopedia, the feast "was instituted in 1513 at Cuenca in Spain, and assigned with proper Office to Sept. 15, 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 Sept. 17."
This assignment of the feast to 8 days after the birth of the Virgin Mary corresponds to the feast of the Holy Name of Jesus, which is celebrated 8 days after the birth of Jesus.
The feast of the Holy Name of Jesus is connected to the Jewish ceremony of circumcision, which was celebrated 8 days after a boy's birth and is recorded in the Bible.
And at the end of eight days, when he was circumcised, he was called Jesus, the name given by the angel before he was conceived in the womb.
Girls do not have the same naming ceremony in Jewish tradition, though girls are named within the first few weeks of birth.
In the 17th century the feast was extended to the universal Church and given another date according to the Catholic Encyclopedia.
After the siege of Vienna and the glorious victory of Sobieski 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.
It wasn't until 1908 that a decree stated, "whenever this feast cannot be celebrated on its proper Sunday on account of the occurrence 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."
At the time it was believed that Mary played a vital role in the military victory and the pope connected it to the feast of the Holy Name of Mary.
Nevertheless, it is fitting to celebrate the Holy Name of Mary within this time frame.