You are thinking of "Nuisance Value," a story by Eric Frank Russell. According to ISFDB's data (I have its listing for this linked to the story title in the previous sentence), it was first published in Astounding Science Fiction (January, 1957). Clicking on the "Astounding" link will take you to where a PDF of the full contents of that issue is stored on Internet Archive.
Personally, I first read this story in the anthology The Seven Cardinal Virtues of Science Fiction, which was first published in 1981 (although I only picked up a copy many years later). Since you think you first ran across this story in the late 70s or early 80s, I strongly suspect you read a copy of that anthology soon after it came off the printing presses.
As it happens, I have reread my copy of that anthology within the last year or so, and so I can assure you that your summary-from-memory of the basic plot is reasonably accurate.
The prison planet, containing approximately 400,000 POWs (mostly of the alien races known as Stames and Aleusines), is called Gathin. As you say, the Stames and the Aleusines, as well as the ones who are running things locally (the Kastans) all cling to an ethos that says a soldier who has been captured by the enemy is now just a contemptible slave who no longer possesses any official rank, nor much in the way of self-respect, and should meekly do whatever labor his captors assign him to do.
The human government (allies to the Stames and Aleusines in this interstellar war) has come up with a psychological trick; a scheme which involves teaching the Stame and Aleusine POWs to start thinking of themselves as belonging in a whole new category: "Gaths," the citizens of the planet Gathin, who need to rise up against their oppressors -- the Kastan garrisons on the planet who function chiefly as prison guards. If the "Gaths" successfully seize control of their planet and announce they are now an independent republic, they will be welcomed into the existing Alliance (Stames, Aleusines, and Humans).
In other words (this next part was hinted at, but not examined in detail in dialogue), after the war, a Stame/Gath veteran could return to his native world while being officially viewed as "one of our brave Gath allies who helped us win the war, and who is now choosing to immigrate to a Stame planet." He could marry a local Stame girl, raise Stame kids, etc., and gradually things would get to the point where the cultures would have changed enough to make it unnecessary to keep mentioning the legal fiction of "he's not a disgraced Stame POW; he's a Gath who bears a remarkable resemblance to a Stame who was in the same school classes with me when we were kids!"
One thing about the story itself: It was written with a strong streak of comedy and some scenes which would be called "slapstick" if they were adapted to film. The human agents who have been maneuvered into being "captured" by the Kastans are not very well fleshed out as characters, but they do exchange lots of quips, etc., while plotting each step of their proposed rebellion. The trickiest thing being to keep the Kastan guards from figuring out that a rebellion is brewing in the first place.
I'll provide a sample of what I mean by "slapstick." At one point, the humans decide to shake things up by having the population of their prison camp be stricken by some scary, mysterious plague. The effect is simulated by having some (not all) of the POW population quietly chew up bits of soap, and then ostentatiously start foaming at the mouth, while falling to the ground and writhing in agony (or so it seems) until they get tired of hamming it up, and close their eyes to become "unconscious." To get the maximum effect, this doesn't all happen at once; different people collapse at different times throughout the day.
After the plague begins, a Kastan officer, Guard-Major Slovits, is trying to get things organized out in the central yard of the prison camp. (Behind his back, the humans sometimes call him "Festerhead." I mention this so you'll understand the reference in this passage.)
Finally the fit were paraded in the yard, the fit being defined as
those able to stand. Two dozen of them dropped in their tracks just as
Slovits opened his mouth to bawl. Slovits closed the mouth while the
end files wearily picked up the bodies and lugged them away. Five of
the luggers swiftly decided that it requires less effort to be carried
than to carry, whereupon they flopped and put on the foaming act. More
end files broke off to take those away.
At that point Slovits came to the end of his patience. Stabbing a
large finger at those still perpendicular, he roared, "All former
doctors, surgeons, hospital orderlies and similar personnel will take
six paces to the front."
Foley marched forward bawling with equal loudness, "One, two, three,
four, five, six." He halted.
Eight Aluesines and eleven Stames did likewise, yelling in unison and
finishing with a simultaneous, "Six." As if that were a signal, two of
them bit the dust.
Slovits glared a moment at the two, his face twitching, his fingers
working around. Then he said to the survivors, "Follow me."
Obediently they traipsed behind him to the office building. Three who
preferred bed to Festerhead shamelessly gained their ends by
collapsing on the way.
Later on, one of the human characters points out that all this was overdone, and Terran prison guards would have quickly figured out it must be a well-organized hoax. But the Kastans just didn't have the concepts of "prison riots" or "organized civil disobedience" on the part of captured enemies, and this massive psychological blind spot could be exploited to the hilt!
