The small metal fasteners used to reinforce the pocket corners of jeans are called rivets.
Rivets are permanent mechanical fasteners made from metal. In classic denim construction, they are pressed through fabric layers and then deformed or capped so they hold securely. At the corners of pockets, where stitching can experience repeated pulling, rivets distribute stress and help prevent the fabric from tearing.
The feature became famous through the workwear associated with Levi Strauss and Jacob Davis. In 1873, the two received a U.S. patent for using copper rivets to strengthen the pockets and other stress points of work trousers. Their reinforced “waist overalls” helped establish the construction details now associated with blue jeans.
Rivets are not the same as studs, eyelets, or grommets. Stud is a broader decorative or fastening term; an eyelet reinforces a small hole, often for a lace; and a grommet is a ring placed around an opening. Jeans may use decorative studs or bar-tack stitching today, but the traditional metal reinforcement at pocket corners is a rivet.