This character is a Other Symbol and is commonly used, that is, in no specific script. The character is also known as wizard, witch, sorcerer and sorceress.
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+1F9D9 prohibits a line break after it, if it’s followed by an emoji modifier.
The CLDR project calls this character “mage” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: sorcerer, sorceress, witch, wizard.
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:
A magician, also known as an archimage, mage, magus, magic-user, spellcaster, enchanter/enchantress, sorcerer/sorceress, warlock, witch, or wizard, is someone who uses or practices magic derived from supernatural, occult, or arcane sources.: 54 Magicians enjoy a rich history in mythology, legends, fiction, and folklore, and are common figures in works of fantasy, such as fantasy literature and role-playing games.