The phases of the moon have been of great interest to humans across time and cultures for far longer than recorded history. The full moon and its effects are easily noticed by all, and if anyone thinks it has no effects, they have only to talk to a police officer, E.R. medical professional or bartender to be enlightened. The dark of the moon is more subtle, yet every bit as powerful. Few experienced fishermen will cast their nets into the sea during the three days of moondark.
Unlike the full moon which lasts for a single night, the dark of the moon is a three-day event. On the last and first days of a moon phase the tiny sliver of visible moon is actually visible only to the very fortunate and those who have the equipment to detect it at the correct time of day. Only on the second, or central, day of moondark is the moon actually 'gone', with only the dark side completely facing Earth. This is the true day of moondark, the liminal day which is not one nor the other, a day out of time. Yet it is a relatively new phenomenon, mostly associated with the New Age movement, to refer to the actual day of moondark as a 'new moon.' It is an inaccuracy which gives rise to a great deal of confusion.
One can argue that it is a matter of semantics, and that in the absence of a visible sliver of moon there is no need to fuss about accuracy. To those who are disinterested in or unable to detect subtle energies this is is surely the case. But for those who are tuned in to the real and palpable energies that affect our planet and the life on it, it can be important to get it right.
In ancient Greece the day of moondark was dedicated to the goddess Hekate, and her sacred Deipnon was celebrated on that day, and is this is still true for modern practitioners. But the 'right' day is not a matter of interest solely to Hellenics. As the full moon and dark moon phenomena are observable to those outside the Pagan community, it makes little sense for those within it to be cavalier about what these energies are and how to work with them.
Moondark is not a day of new beginnings. It is a threshold, a time out of time in which outward directed thoughts and actions have little effect, but internal alchemy is potent. For those wishing to harness the power of new beginnings and fresh starts, the new moon, i.e. the third day of moondark, is a much more practical and sensible approach. Moondark itself is a day to go within, to be still, and to prepare for action, not to begin.
Some calendar days are a matter of mutual choice within a community. New Year's Day on the Gregorian calendar is just such a day. Many people, for religious or societal reasons, consider their years to end and begin at other times. But for the vast majority of the world January 1st is the start of the new year. We are free to accept this, or arrange our own calendrical observances as we please. But moon phases are not subject to popular opinion. No harm is done by referring to 'moondark' as a 'new moon', but for those who actually wish to sense, use and flow with real energies that have a real effect on their lives, it behooves them to understand the subtleties and powers of natural energies. Social media memes notwithstanding.