I'm pretty sure that is a Muncie "M2x" of some type; M21, M22, etc. Take of the shift cover and see if the gears have straight teeth or helical teeth, start there. The grooves on the input spline may mean something, but maybe not, as that shaft looks gold-colored and may be an aftermarket piece. Just search online for "muncie trans" or "muncie 4-speed", you will find oodles of info.
If you are going to use that trans on the engine, step up to a dual-disc clutch. The BBC likes to eat up single-disc clutches...
Well, I just peeked online. It seems the Muncie M-series was derived from the Borg-Warner T-10 and they look very similar. Is the case cast-iron? If so, then I think it is more likely a T-10; I'm thinking the Muncies were all aluminum cases. Again, lots of info available on either trans family!