The phase of the moon that happens after we see less of it at night is called the waning crescent.

Here's a breakdown:

* Waxing phases: The moon appears to be growing larger each night.

* Waning phases: The moon appears to be shrinking each night.

* Crescent: The moon appears as a thin sliver of light.

So, when the moon is waning and appears as a thin sliver, it's in the waning crescent phase.