We even have an official photo, showing triple tailpipes surrounded by a similarly-shaped surround made of what looks to be aluminum, possibly titanium. It's obviously nestled in the rear of the P15, since side-pipes wouldn't look like this. Otherwise, there's not much to glean from it. It's nice to know, however, that the BP23 won't be alone at the top of McLaren's range.
We'll be watching for updates on the P15 (and the BP23) and bring you whatever we find. Hopefully that'll include better names, the sooner the better.