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Might be a downplayed example of Going Native or Mighty Whitey. There ought to be a "Friend of the tribe" or "honorary Klingon" trope, but I don't seem to be finding any examples.
As far as existing tropes, I'd file Jadzia Dax as a special case of Going Native; the reason that she was so quickly accepted is that Dax lived among the Klingons as Curzon Dax. (For non-trekkies, trill are best described as a symbiotic form of Puppeteer Parasite, Dax being the symbiote half of the personality)
There still could be a subtrope here for the idea of being formally claimed by said group; for instance Curzon Dax not only took up the Klingon's ways and lived among them, he was formally adopted as a blood-brother by several of his Klingon comrades.
Is there a trope for when someone is considered an honorary member of another race?
One example I can think of is Jadzia Dax from Star Trek: Deep Space Nine, who was respected among Klingons in spite of being a Trill and was welcomed into a Klingon house when she married Worf.