This character is a Other Symbol and is commonly used, that is, in no specific script. The character is also known as frustration and disbelief.
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+1F926 prohibits a line break after it, if it’s followed by an emoji modifier.
The CLDR project calls this character “person facepalming” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: again, bewilder, disbelief, exasperation, facepalm, no, not, oh, omg, person, shock, smh.
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 facepalm is the physical gesture of placing one's hand across one's face, lowering one's face into one's hand or hands or covering or closing one's eyes. The gesture is often exaggerated by giving the motion more force and making a slapping noise when the hand comes in contact with the face. The gesture is found in many cultures as a display of frustration, disappointment, exasperation, embarrassment, horror, shock, surprise, exhaustion, sarcasm, shame, or incredulous disbelief.