I'm really, really, really regretting throwing out my old tables. At the time, I figured I could salvage the parts. But, my wife didn't want them cluttering the house, and I figured there was nothing I could really use those arms on.... that is.... until now.
The company that makes that lamp is called Wildon Home. I did a google search, seeing if I could find the Wildon Home website. I figured I could contact them directly for replacement parts, or just to get the name of that piece. However, I have only been able to find websites that sell Wildon Home products, not an actual site for the company.
Maybe you gentlemen will have better luck?