Algis Budrys, "Who?" (1955), related to American Science Fiction: Nine Classic Novels of the 1950s:
To explain the weird attribution above, the short story "Who?" was later expanded by Budrys into the novel Who?, which is included in the LoA collection of 1950s American sf.
Though, as the headnote says, Budrys's background isn't American: he came over because his father was in the Lithuanian government, and while they were in the US, Lithuania got taken apart by the Soviets and the Nazis (and then the Soviets again). So it's not a surprise (says whoever writes these LoA page) that Budrys's fiction often revolves around themes of identity. The LoA page also includes the excellent fact that Budrys came over when he was 5 and became an American citizen when he was 65; what they don't say is that he was an officer in the Free Lithuanian Army for most of his adult life, which was probably a less-than- (or other-than-)actual organization.
The excellent Tim Powers compares the story to the novel as a sketch to a masterpiece, and since I haven't read that novel, I will have to take his word for it.
The basic story here is summed up in a few sentences by the LoA headnote, but takes a few pages to become clear in the story itself: an American scientist (on the moon) was blown up in an accident, rescued and rebuilt and returned by the Russians--or was he? Because the largely mechanical man (with the nuclear pile in his chest powering his cyborg body, like Iron Man) might just be a Soviet agent. And the Americans have no physical way to check.
The story pings some "but what..." questions, but Budrys largely takes care of these: Why would the Russians rebuild him? To interrogate him. Why would they return him? Because of diplomatic pressure and perhaps as part of a larger diplomatic gambit. Why can't the Americans figure this out? Because their cyborg technology is not as advanced as the Russians. Etc.
So it's a well-crafted set-up, but Budrys himself said the ending was weak. Here's the ending: the guy assigned to figure out whether Dr. Martini is really a kid from New Jersey walks into the holding cell and calls him a "wop." And without thinking about it (we're told), Martini jumps up to attack, just as he would've done growing up in ethnically diverse but segregated New Jersey.
Budrys wants to make it clear that ethnic slurs are not restricted to America, as the main guy also thinks that, if "Martini" was really a Russian plant, he'd probably spent his youth fighting with other ethnics in the Soviet Union. Which is funny, in a strange, sad way: no matter your economic situation, there's going to be kids beating each other up because the other kid is a wop or an Asiatic.
It reminds me of Murray Leinster's "First Contact," which is a similar puzzle story: humans and aliens meet, they want to exchange peaceful data, but neither can trust the other. The result, both of them put into play the exact same plan about killing the other--which means that we really can trust each other, since we're so alike. Then at the end, two communication officers from the different species end up telling dirty jokes. It's a fun message of universalism: every (male) army tells dirty jokes about women, every community has some ethnic strife.