This Sunday (or January 2 if there is no suitable Sunday) has been celebrated as the feast of the Holy Name of Jesus since the sixteenth century.
In the 1962 revamp of the Benedictine calendar, however, this was replaced by liturgical wreckovators, by the 'Second Sunday of the Nativity', complete with new texts. The 1962 Roman Missal however remained unchanged, leading to an odd disjunction between the Benedictine Use and the Roman. The wreckovators did try again temporarily succeed in their aims with respect to the Roman rite: the 1970 Missal made the feast optional only. But it was restored in the 2002 calendar (albeit this year on January 3 rather than the Sunday, which has, in most places become Epiphany Sunday aka Eleventh Day!).
Accordingly, the omission of the feast in the Benedictine 'traditional' calendar of 1962-3 is anomalous. If you attend a Roman EF, or your monastery includes the older feast in its calendar, and so want to celebrate the Feast of the Most Holy Name of Jesus, you can find the (Latin) texts in the Antiphonale Monasticum, at pages 276 ff. Alternatively you could either use this to say the Office devotionally, or say the Office according to the Roman Breviary (Divinum Officium has the text).
Either way, Vespers on Sunday is for the following feast of the Epiphany, as Nativitytide officially finishes at None on Sunday this year, though of course the season of Epiphany is still part of the broader Christmas season.
Readings at Matins
The readings for Matins this Sunday (according to the 1962 Benedictine Breviary) are as follows:
Nocturn I: Romans 1-11 (note that reading 3 for January 5 is split in two to make four readings, and responsories are for the Sunday)
Nocturn II: Sermon of St Augustine
Nocturn III: Sermon of St Jerome on Matthew 9:2
Gospel: Mt 2:19-23
The Office this week in summary
Sunday 5 January – Second Sunday after the Nativity, Class II [EF: Most Holy Name of Jesus]
Monday 6 January – Epiphany of Our Lord, Class I
Tuesday 7 January – Class IV
Wednesday 8 January – Class IV
Thursday 9 January – Class IV
Friday 10 January – Class IV; St Paul the First Hermit, memorial
Saturday 11 January – Saturday of Our Lady (Sat 2 of Jan) [EF: Commemoration of St Hyginus]