Welll, the good news is you came to the right place...the fountain of all-knowing gurus! Further good news is that we WILL figure it out. But at this time, I don't have the answer! I am only 67, and came to plumbing relatively late in life. We have a few guys on here who will nail that down.
The innards resemble Delta/Peerless or Valley. But the escutcheon screw holes above the stem are not right, at least not for the ones I can put my finger on. I am thinking the handle and/or the escutcheon may be replacements, hence no name. Based on the stem, I think certain Valley or Delta 600 handles might work.
Stay tuned, and if you wouldn't mind, take one more picture with the chrome plate removed. Some one will nail this down for you!