Cyrenius, or Quirinius
Archimandrite Nikifor’s Biblical Encyclopedia
(Latin Quirinus) (Luke 2:2) - a Roman governor of Syria, dated by the source to 759-764 from Rome's foundation. It says he governed Syria twice, first about four years before Christ's birth and at the time of it, and again several years afterward. Under Augustus's command an enrollment was made throughout the land during his government; Joseph and the Virgin Mary therefore went to Bethlehem, their ancestral city, where the Christ Child was born. Josephus also writes expressly of an enrollment under Quirinius (Antiquities 18.1).