This often comes up in movies, but I can hardly find any real cases, except for the "Illegals Projects" - but that doesn't seem like high-stake espionage, let alone successful.
I'm thinking specifically of cases where the spies had to hide their substantial knowledge of an entire other culture, being fluent in the given language, etc., e.g. when they come from another country (and they pretend to be either native to the country they spy on, or to have come from a third unrelated country).
Any examples are appreciated, especially with a link/reference to the source where the details are described.
(You are welcome to add any examples as answers. I guess this is not a question that has a very definitive answer but I'll upvote any good examples.)
Question: Were there any important spies in modern history who had to conceal their true nationality (or culture)?
While not an especially important spy, and not involved in concealing one's "national" identity, I'm going to go with the story which inspired the play M. Butterfly. Where a man concealed his gender from someone he recruited for over a 20 year period.
The Chinese Spy Shi Pei Pu. While not an important spy it's a great story. Shi Pei Pu initially convinced a French embassy clerk Bernard Boursicot that he was a woman dressed as a man. Then had a 20 year affair with him, and even pretended to have his baby. The baby Shi Pei purchased from a hospital. The affair led Boursicot to hand over as many as 150 French embassy documents to the Chinese secret service over 20 years, before Boursicot returned to France in the early 1980s. Boursicot brought Shi and his “son” to France, at which point Shi Pei's deception fell apart.
Shi Pei Pu
Shi and Boursicot were each convicted of espionage in 1986 and sentenced to six years in prison. Shi was pardoned by President of France François Mitterrand in April 1987, as part of an effort to defuse tensions between France and China over what was described as a "very silly" and unimportant case. Boursicot was pardoned in August of that year.
The affair inspired David Henry Hwang's 1988 play M. Butterfly. B.D. Wong played Song Liling, a Chinese opera singer and spy based on Shi Pei Pu, in the original Broadway production of the play.
Eli Cohen is an excellent example. Debatable is Mata Hari. Debatable in the sense that she possibly/likely wasn't a spy. In all other aspects (culture, language, behaviour, etc.) she was fluent in Dutch, German, English and French.