January (the old calendar) of the old calendar is called 'shogatsu' (in the old calendar, 'shogatsu' is the formal name and 'ichi-gatsu' [meaning January] is another name), and the kyu-shogatsu (the old new year's day) is also called 'shotan'.
また、旧暦1月(旧暦)のことを「正月」と呼び（旧暦では「正月」が正式名、「1月」が異名である）、旧正月を「正旦」ともいう。