Later Adobe productized this. Originally it was called "PostScript Distiller", but then they introduced some incompatibilities with PostScript and renamed it "PDF".
Fascinating. So PD in PDF came from Postscript distiller? All these years... I did not know that.
Sounds like an unanswerable question; it would be surprising if anyone reliably remembered earlier expansions for the initialism. Distiller remains an Adobe product.
The official name when PDF was launched as "Portable Document Format". I have no idea if that was a "backronym" for some internal project name.
Postscript printers could often deliver more pages per minute mechanically than their processing could deliver.
Lancaster showed how to basically compile and pre-process a book into a big postscript file that minimized the printer compute requirements. Load up an Apple //e machine with some respectable storage and it could deliver books on demand, printing at near max print speed.
Damn cool.