All of the above (except Thermal Block Box... no idea what that means). There is no "proper" name that I've been able to determine, everyone calls it whatever they heard the first time.
At the risk of repeating my stories, I was once challenged by my HR department on the use of the term "motor peckerhead" in a training presentation. Someone complained about my use of "inappropriate terminology" because apparently someone was under the impression that the name was derived from a not-so-genteel anatomical reference. I countered that it was a commonly used industry term and had no such connotation other than in the minds of some people, so they (HR) wanted me to prove it. After a lot of research, I could not find an officially sanctioned source of the term, and in fact found a lot more references to the inappropriate meaning. I did find however a reference to the term possibly being a derivation of the term "picker box", which was apparently something used in fruit picking that had a similar appearance. But because I could not find a solid reference to the term peckerhead having another meaning, I had to change it on my training presentations. I used the term "motor termination box". I found out however in that process, that there is no "official" term for it anywhere, even in NEMA MG1 specifications where they use both "terminal box" and "conduit box" interchangeably (never peckerhead or connection box however). So from that you could narrow it down to those two terms I suppose.
As to a resource for replacements, generally these are something that the motor mfrs make themselves. I have had to order replacements for rusted out ones and never found a 3rd party supplier. But I would order them from whomever would sell them to me, they all tend to use common mounting hole patterns so one from a Baldor motor worked on a GE motor of the same frame size. The NEMA MG1 specifications dictate the minimum size, orientation and mounting of them.
" We are all here on earth to help others; what on earth the others are here for I don't know." -- W. H. Auden