"The Refinery", the "Nostromo refinery" or (possibly) "The Bismark"
There's an extremely extensive discussion of the concept, concept design and physical design process for the ore refinery here. In short, the refinery doesn't seem to have collected an official name or designation. It's merely referred to as "the refinery" in interviews, the film, the film novelisations, graphic novels and the various Alien factbooks.
Sealed cameras on the battered skin of the Nostromo began to move
silently in the vacuum of space, hunting through infinity for hints of
a warm Earth. Secondary cameras on the Nostromo's cargo, a monstrous
aggregation of bulky forms and metal shapes, contributed their own
line of sight. Inhabitants of an earlier age would have been
astonished to learn that the Nostromo was towing a considerable
quantity of crude oil through the void between the stars, encased in
its own automatic, steadily functioning refinery.
Alien: Official Novelisation
and
FF: Who designed the refinery?
Ridley Scott: I did. I didn't want a conventional shape, so I drew a sketch and handed it to the model makers. They refined it, as it
were, and built the model. I originally drew it upside down, with the
vague idea that it would resemble an inverted cathedral.
Fantastic Films #12
and
Ridley Scott: I saw it as a gigantic maneuverable jump jet. Therefore it was able to get wherever it wanted on various planets,
landing in a quite narrow, rocky terrain. So that's the only
streamlined object in the whole thing. The refinery itself is a
conglomerative mountain of technology.
Fantastic Films #12
and
Phil Pearson: Brian gave us the relevant frames of... the Nostromo lander and refinery. In Ridley's storyboards, they were very gothic in style and the first job we had to do was, erm, a tower for the refinery from Ridley's black and white board. We made one tower, one protoype tower, that was Simon Deering and myself 'putting that together. It was, as I say, very very gothic. You could, I was trying to mimic what Ridley had drawn,
...
He proved a point that they didn't have to be black and they could be black lit to look silver. and silver look like black. That tower ended up on the Nostromo refinery and it seemed to be one of Ridley's favourites after all that time. If you watch the film very closely, you'll find that the towers do move 'round quite a bit but not always in the same place because Ridley would say "Oh Get us that tower, put it in to this corner, I'm over here shooting," So, he did have his favourit pieces of Wiggetary.
ALIEN Makers Documentary I
That all being said, it does however, seem to have picked up a nickname based on James Cameron's description of it; The Bismark.
Dennis Lowe: At that same time in the workshop Ridley was talking about his first concept of the refinery and he was describing an actual oil refinery with pipes and spires, eventually the term 'Battleship Bismarck in space' came up to describe the detailing of the model.
ALIEN Makers Documentary IV
and
Dennis Lowe asked "you mean like the Bismark in space?"
Ridley replied "that's right, I want it just like the Bismarck in
space"
ALIEN Makers Documentary IV