December 26 through 28 are feast days of St. Stephen the Martyr, St. John the Apostle (who was willing to die for his faith but lived a long life), and the Holy Innocents. Thus, three days of the Octave of the Nativity remember different kinds of martyrs.
Interestingly, the best known blessed named for the Nativity in religious life was also a martyr, as was an Augustinian named for the Nativity whose cause for beatification is pending.
Blessed Dionysius of the Nativity (also called "Bl. Denis of the Nativity") was a Discalced Carmelite missionary who was tortured and martyred by Muslims in 1638 on the Malay archipelago (Sumatra, Indonesia). The cause for his canonization is pending. A Frenchman, he was born Pierre Berthelot. His memorial is November 29.
Anthony of the Nativity, a contemporary of Bl. Dionysius of the Nativity, was one of the Mombasa Martyrs, Portuguese Augustinians who died in 1631 in what is now Kenya. Their cause for beatification was opened soon after their deaths and is still pending.
Of course, not all blesseds named for the such mysteries are martyrs. As an example, Bl. Marie of the Incarnation (also called "Bl. Mary of the Incarnation") was another contemporary of Bl. Dionysius of the Nativity. She too was a French Discalced Carmelite, born Barbe Avillot. A wife and mother of six, she became a lay Discalced Carmelite after her husband's death. She died of natural causes in 1618 at the age of 52. Her memorial is April 18.