Hi Master468,
If you look in the Ashley Book of Knots (ABOK) you will find what looks like this hammock clew as #3819 or #3820. #3819 is called the Sword Mat Ring Clew and #3820 is the Sailor's Hammock, strictly not a separate hammock clew, but a way of putting the canvas together for the hammock, according to ABOK. The ring in your photo does not appear to have been hitched over. Does that help?
SquareRigger