It's called an apron?
I think Brooks has done this a couple different ways over the years. I have in my hands, at the moment, a Swallow dated C60 on which the leather has two tabs that meet under the center of the saddle, where they are riveted to a small steel plate (about 1 ¹/4" x 1¹/8"). So this saddle is done the same way, except that the plate is copper, rather than steel, but you can't see it anyway.
I was guessing as to what to call it. "Tabs" sounds a lot better then "apron."