This character is a Other Symbol and is commonly used, that is, in no specific script. The character is also known as mermaid and merman.
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+1F9DC prohibits a line break after it, if it’s followed by an emoji modifier.
The CLDR project calls this character “merperson” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: creature, fairytale, folklore, ocean, sea, siren, trident.
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: 🧜︎ The character can be changed in appearance, if it is followed by an emoji modifier. See the Emojipedia for more details on this character’s emoji properties.
The Wikipedia has the following information about this codepoint:
Merfolk, Mercreatures, Mermen or Merpeople are legendary water-dwelling, human-like beings. They are attested in folklore and mythology throughout the ages in various parts of the world. Merfolk, Merpeople, or simply Mer refers to humanoid creatures that live in deep waters like Mermaids, Sirens, Cecaelia etc.
In English, female merfolk are called mermaids, although in a strict sense, mermaids are confined to beings who are half-woman and half-fish in appearance; male merfolk are called mermen. Depending on the story, they can be described as either ugly or beautiful.
Chinese rényú (人魚) stands for "merfolk", but in ancient geographical or natural historical tracts, the term referred to "human-fish" or "man-fish" purported to inhabit rivers or lakes in certain parts of China. The Japanese analogue ningyo (人魚) likewise translates to "merfolk" while, at the same time, having also applied to various human-like fish recorded in writings from medieval times into the Edo Period.