What is the name of this recliner couch screw holder?
Doesn't really matter what they're called. They're almost certainly proprietary and shown in an exploded parts diagram somewhere with a number next to them. You won't find them in hardware stores (real or online).

You'll need to get in touch with the manufacturer one way or another, or you'll need to fabricate something that performs the same function without the efficiency of design afforded by that exact part. It could be that a block of nylon with dimples drilled in each face does the job, for example, or maybe a sleeve nut and some bolts.