But what about The Hu?
Eric the Eel is from Equatorial Guinea.
Paul Rusesabagina may be the most famous person from Rwanda. If you don’t immediately recognize the name, he’s the guy Don Cheadle played in Hotel Rwanda.
Sadly, Idi Amin may be the most famous Ugandan.
Likewise, Jean-Bédel Bokassa may be the most famous person from the Central African Republic (or the Central African Empire as he called it).
I would say Aung San Suu Kyi is more famous than U Thant.
Derek Walcott, a Nobel Literature Prizewinner, was from St. Lucia.
As were J. R. R. Tolkien, Charlize Theron, Basil Rathbone, and Trevor Noah.
I think you’re confusing Vijay Amritraj, a tennis player, and Vijay Singh, a golfer.
Bangladesh, Finland, Czechoslovakia, Philippines, South Africa, Austria? It’s beginning to look like Dopers consider most countries in the world to be obscure. Maybe you could share some famous Germans or Pakistanis or Brazilians next.
My go-to country for obscurity is Laos. Think: When’s the last time you heard anything from Laos? But now the challenge is to name a famous Laotian. Souvanna Phouma? Prime minister in the '60s and '70s.
If you cite Jamaica without naming Bob Marley, you’re dead to me.
Nobel prize winning author Sir Vidiadhar Surajprasad Naipau aka V.S. Naipaul was born and raised in Trinidad.
When was the last time you saw Bangladesh in the news?
I think the question in the OP is too vague. Does people mean living ones or any human ever? How famous do you have to be to be included? How little noticed does the country have to be? How long do they have to live in the country?
I too can name people from countries.
What about Nadia Comaneci? At least the average Doper should be of an age where she would be remembered well. (And, well, if you remember that, you probably also remember the Ceaușescus, for better or worse.)
I had no idea Zamfir was Romanian, though.
As were J. R. R. Tolkien, Charlize Theron, Basil Rathbone, and Trevor Noah.
Nelson Mandela, anyone? Desmond Tutu?
I wish to nominate Rihanna. Born and raised in Barbados!
There you go. That’s what this thread is looking for.
Another famous Senegalese:
West African music and musicians are well known to “world music” fans - how about Ali Farka Touré from Mali?
Iceland is mentioned above - it punches well above its weight culturally - Björk, Sigur Ros, Vikingur Olafsson, Olafur Eliasson, thriller writers like Arnaldur Indridason.
Since no-one else has mentioned it, there is a game about how many famous Belgians you can name. Leaving politicians aside, there’s Jacques Brel, Georges Simenon, René Magritte (and erm…)
Eddy Merckx! Kevin de Bruyne. Adamo (ok, a bit obscure nowadays, but big in the 70s). And Hercule Poirot (ok, cheating 
).
Django Reinhardt, the original shredder. 
That’s a good one!
I doubt most people can name anyone from Mongolia aside from Genghis Khan.
While I suspect that’s true, there are many famous sumo wrestlers from the actual current Mongolia, as opposed to the historic version before modern statehood concepts were formalized. The most famous would be Hakuho, who, alongside Don Bradman if we’re talking about people most Americans never heard of, should be part the discussion of the most dominant athlete ever.