Hmm.. for a second I thought, "maybe they're just not sticking with the original color names and are using 'Tan' as an umbrella term for any shade of brown," but I just checked the reloved bags that were released today and there does seem to be a distinction between the colors. British tan bags with brass hardware are under "Brass/Tan" while the mahogany bags with brass are listed as "Brass/Brown." This makes me think they might have accidentally sent you the wrong color. Doesn't really matter if you're happy with bag and the color, but if you did have your heart set on the British Tan, you could maybe contact customer service? I'm not sure if they could resolve it for you or what solution they would offer you, but I guess it wouldn't hurt to ask if you really wanted the other color.
Also, regarding whether or not its a fake, you could always have it authenticated here just to be sure. If by any chance it were a fake, I'm pretty sure I heard that
Coach allows the reloved bags to be returned.