The Hebrew word for moon, “lebanah,” is a feminine noun. The Hebrew for “full,” “maw-lay,” is male yet can mean “pregnant woman.” While the New Moon Sabbath was overseen by the male Levite Priests, it is believed that the Full Moon Sabbath may have been overseen by the Levite Priestess until these daughters of Miriam were shut away.
In modern Judaism, there are two full moon holy days.
The first is Tu B'Av (literally “the fifteenth of Av”), a holy day of love. The second is Tu BiShvat in Shevat, the New Year of the Trees. These likely reflect ancient Mother Goddess holy days that were rejected when Judea became monotheistic.
See 2 Moses 26:22, 29:5; 4 Moses 34:30-32, 38:7-8, 11-12; Psalm 81:3; Doctrines of the Saints 123.