This character is a Math Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it acts as Other Neutral. When changing direction it is mirrored. If its East Asian Width is “narrow”, U+2202 forms a word with similar characters, which prevents a line break inside it. Otherwise it allows line breaks around it, except in some numeric contexts. The glyph can be confused with 8 other glyphs.
The CLDR project calls this character “partial differential” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: differential.
The Wikipedia has the following information about this codepoint:
The character ∂ (Unicode: U+2202) is a stylized cursive d mainly used as a mathematical symbol, usually to denote a partial derivative such as $\partial z/\partial x$ (read as "the partial derivative of z with respect to x"). It is also used for boundary of a set, the boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold. It should be distinguished from other similar-looking symbols such as lowercase Greek letter delta (δ) or the lowercase Latin letter eth (ð).