What phase of the moon occurs about 3 days before the new moon?
There is no special name for that.
The waning crescent moon occurs after the third quarter moon and before the new moon.
It will be the Full Moon again, more or less. The time for one complete cycle of the Moon's phases is just a few minutes over 29 and a half days. Exactly 29 days after the moment of the start of the Full Moon phase, it's about 12 hours 45 minutes before the moment of the start of the next Full Moon.