Hergé!
Halldór Laxness, Sjón, Snorri Sturluson, Magnus Magnusson, Leif Ericson, and Bobby Fischer (who moved to Iceland late in his life)
Eddy Wally if you’re of a certain cultural niche. But probably not famous enough more generally for this purpose.
Omar Sharif was from Egypt.
And if you take fame in the Middle East as sufficiently significant, then there’s Umm Khultum from Egypt and Fairuz from Lebanon.
Beats me that I’ve never heard before of Eddy Wally. Even if he called himself the “Voice of Europe”, he seems to never had made it to Germany, although German TV of the seventies was full of all-European stars. THE Belgian singer of that time in Germany was the aforementioned Adamo.
Well I must admit he featured a lot in anAnglo-French TV show called Eurotrash, along with the likes of Lolo Ferrari. I was rather joking (it’s been discombobulatingly hot in London today).
Ok, I may never have heard of Eddy Wally, but of course I know Lolo Ferrari 
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Estonia: Arvo Pärt. World famous ‘minimalist’ composer.
My first thought was Orly Tait from Moldova, but she hasn’t been in the news much in the last decade.
A lot of the countries mentioned above are not anywhere “least-noticed” to me.
Through his mother, Dwayne Johnson is half-Samoan, so I’d nominate him.
Except for the fact that Franz Kafka was born in Prag, then: Oesterreich-Ungarn … (today: not so much, anymore) …
Augusto Pinochet, Chile
I assume most right thinking Chileans would prefer to be remembered for Pablo Neruda rather than for that individual, sorta like the Austrians with Mozart and the other one…
depends vastly on your definition of “right thinking”, I guess
Yup, right as in correct or right as in political ideology.
Or Isabelle Allende.
Born in the U.S., though. Otherwise, I’d nominate Troy Polomalu.
Isabel 
A couple of tenors internationally famous in the operatic world are Juan Diego Flores from Peru and Joseph Calleja from Malta.
Action film star Jean-Claude van Damme is also Belgian.
Kim Clijsters and Justine Henin! OK, I guess you gotta be into tennis somewhat to remember those two in the early 2000s, but they were on top of the world back then, and Belgian! I loved watching those two.
If you want to stump people with a good musical trivia question, ask them what country Freddie Mercury was born in.
Tanzania