This character is a Other Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its East Asian Width is wide. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. U+1F31D offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “full moon face” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: bright, face, full, moon.
This character is designated as an emoji. It will be rendered as colorful emoji on conforming platforms. To reduce it to a monochrome character, you can combine it with Variation Selector-15: 🌝︎ See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
The full moon is the lunar phase when the Moon appears fully illuminated from Earth's perspective. This occurs when Earth is located between the Sun and the Moon (when the ecliptic longitudes of the Sun and Moon differ by 180°). This means that the lunar hemisphere facing Earth—the near side—is completely sunlit and appears as an approximately circular disk. The full moon occurs roughly once a month.
The time interval between a full moon and the next repetition of the same phase, a synodic month, averages about 29.53 days. Therefore, in those lunar calendars in which each month begins on the day of the new moon, the full moon falls on either the 14th or 15th day of the lunar month. Because a calendar month consists of a whole number of days, a month in a lunar calendar may be either 29 or 30 days long.