Chicago Assyrian Dictionary “S” page 313 (abbreviations are expanded for clarity):
siriam (sariam, siriannu, širiam, širˀam, širˀannu) substantive masculine and feminine; [meanings] 1. leather coat, often reinforced with metal pieces, 2. (a garment); [attested in the following dialects and archaeological sites:] Middle Babylonian, Boghazkuei, Early Assyrian, Nuzi, Standard Babylonian, Neo-Assyrian, Neo-Babylonian; foreign word; pl. sarijamāti, širˀamēti.
In earlier and more northerly sources, siriam is a common word for armour as worn by men, horses, or chariots and made of leather, bronze, or iron. In Babylonia in the first millennium, which I am more interested in, it had wider connotations. Sarijamāti are often written with the determinative TÚG “cloth, clothing,” cost about one shekel of silver apiece, and can be worn by soldiers or by slave girls. The famous cavalryman Gadaljama requested an iron širˀannu along with some arming garments. This broad range of meanings from “clothing” to “armour” is common in armour terminology, as people imitate armour in lighter materials or shape armour like fashionable clothing.
One day our knowledge of these terms will be aided by the publication of lexical texts which defined or translated cuneiform expressions for new or scholarly scribes. Unfortunately, few of these texts have been published from Babylonia in the first millennium BCE.
Edit 2022-09-12: fixed formatting broken when WordPress introduced the block editor