There are two ways of reckoning a lunar month- 'purnimanta' and 'amanta'. In the former, the first day starts after the full moon; and in the latter, after the new moon. Though the amanta reckoning is more common now, the purnimanta was very much in vogue in the earlier days.
According to this purnimanta reckoning, Phalguna purnima was the last day of the year and the new year heralding the Vasanta-ritu (with spring starting from next day). Thus the full moon festival of Holika gradually became a festival of merrymaking, announcing the commencement of the spring season. This perhaps explains the other names of this festival