This character is a Currency Symbol and is commonly used, that is, in no specific script.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it is written as end of a European number, e.g., a currency symbol, from left to right. When changing direction it is not mirrored. U+20A2 prohibits a line break after it, if it is followed by a number.
The CLDR project calls this character “cruzeiro” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: BRB, currency.
The Wikipedia has the following information about this codepoint:
The Cruzeiro sign ⟨₢⟩ is a typographical abbreviation or ligature consisting of a capital Latin letter ⟨C⟩ with a nested lower-case letter ⟨r⟩, connected in a single glyph.
This glyph occasionally replaced the ⟨Cr⟩ part of the currency symbol for the first Brazilian cruzeiro, created in 1942, whose official symbol was "Cr $" (two separate letters, a space, and a single-stroke dollar sign). It could also have been used for other Brazilian currencies called "cruzeiro" that were official in 1942–1986 and 1990–1993.
Some typewriters and cash registers produced for the Brazilian market had ⟨₢⟩ keys, and it was available in some typefaces.
The Brazilian keyboard layout ABNT-2 specified by the ABNT standard NBR 10346 specifies that the ⟨₢⟩ symbols should be available through the combination AltGr+C. However, since it refers to discontinued currencies, it is hardly ever used, and may not work.
The symbol was included in the Unicode standard (name "CRUZEIRO SIGN", code point U+20A2) since its first version.