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+1F409 offers a line break opportunity at its position, except in some numeric contexts.
The CLDR project calls this character “dragon” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: animal, fairy, fairytale, knights, tale.
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:
A dragon is a magical legendary creature that appears in the folklore of multiple cultures worldwide. Beliefs about dragons vary considerably through regions, but dragons in Western cultures since the High Middle Ages have often been depicted as winged, horned, and capable of breathing fire. Dragons in eastern cultures are usually depicted as wingless, four-legged, serpentine creatures with above-average intelligence. Commonalities between dragons' traits are often a hybridization of feline, reptilian, mammalian, and avian features.