Here is the oration that the Church prays in the Mass and Office of the Feast of the Holy Name of Mary:
Concéde, quǽsumus, omnípotens Deus: ut fidéles tui, qui sub sanctíssimæ Vírginis Maríæ Nómine et protectióne lætántur; ejus pia intercessióne, a cunctis malis liberéntur in terris, et ad gáudia ætérna perveníre mereántur in cælis.
Here is my translation:
Grant, we beg Thee, Almighty God, that Thy faithful, who rejoice under the Name and protection of the most holy Virgin Mary, may be freed by her loving intercession from all evils on earth, and may merit to arrive at eternal joy in heaven.
Here is the translation from the Divinum Officium site:
Grant we beseech thee, O Almighty God, that thy faithful people, who rejoice in the Name and keeping of the most holy Virgin Mary, may by her Motherly prayers be freed from all ills upon earth, and worthily attain unto thine everlasting joy in heaven.
We “rejoice” under Our Lady’s “Name and protection,” for it is a privilege and a grace to be placed under that Holy Name and protection. One may find here a lovely icon with an explanation of the Byzantine custom of venerating “the Protection of the Theotokos”; it is a fine Eastern Christian complement to this Roman prayer.
I strongly recommend reading Saint Bernard’s lovely meditation on the Holy Name of Mary.
May we all dwell under the protection and Name of Mary to avoid all evils in this life and enjoy the everlasting beatitude of Heaven!