Can anyone identify/name this plumbing component?
I discovered the answer to my own question. I went to the Delta™ site after looking up Delta™ faucets on Amazon™, and discovered that this widget is indeed an integral part of the spigot -- it allows Delta™ sprayers to be plugged in and functions as the diverter. Or the diverter receptacle. 

Unfortunately Delta™ doesn't offer a mating sprayer in the nickel finish that they sold this faucet in.

Alaska Man gets the kewpie doll for suggesting that I look at the faucet manufacturer website. I had been assuming that the widget was a separate component, and had not ever considered the idea that it was part of the faucet!