Synonyms for January 1 (same or very similar meaning)
WordNet sense 1 ((Roman Catholic Church and Anglican Church) feast day celebrating the circumcision of Jesus; celebrated on January 1st):
circumcision, Feast of the CircumcisionWordNet sense 2 ((Roman Catholic Church) a holy day of obligation):
Solemnity of MaryWordNet sense 3 (the first day of the year):
New Year's Day, New Year'sFrom the ODE community, based on WordNetadd/edit