Nitpick: It’s Tanzania now, but when Freddie Mercury was born it was the Sultanate of Zanzibar.
Yes, it may have had a name change and a new constitution, but it’s still the same country. 
Bangladesh is the eighth largest country in the world by population, and is often in the news because of its repeated and disastrous floods. However I find that I don’t recognise the names of any famous people born in Bangladesh, except perhaps William Beveridge the founder of Britain’s NHS, and he doesn’t really count. I’m sure this is a shortcoming on my part.
Haing S. Ngor is probably the most famous Cambodian if you don’t count genocidal dictators.
Rapper/singer Niki Minaj is from Trinidad and Tobago.
Plus, Ava Max is American-born of Albanian immigrants.
Muhammad Yunus, as mentioned above, is probably the most famous Bangladeshi. He’s famous for pioneering microcredit (from Wikipedia, “the extension of very small loans (microloans) to impoverished borrowers who typically lack collateral, steady employment, or a verifiable credit history. It is designed to support entrepreneurship and alleviate poverty. Many recipients are illiterate, and therefore unable to complete paperwork required to get conventional loans. As of 2009 an estimated 74 million people held microloans that totaled US$38 billion. Grameen Bank [founded by him] reports that repayment success rates are between 95 and 98 percent.”)
Other than Tenzing Norgay, are any Nepalis well-known?
For Chile, the Google Ngram Viewer has Salvador Allende ahead of Pablo Neruda and Augusto Pinochet, with other famous Chileans I can think of well behind. Pedro Pascal is a bare blip there, but their data only goes up to 2019, which is before Pascal became really famous for The Mandalorian (premiered November 2019) and The Last of Us (January 2023).
Are there any famous people to have come from Nagorno-Karabakh, South Ossetia, Abkhazia, Transnistria, Western Sahara, Northern Cyprus or Somalialand? I’m assuming there are zero famous Bir Tawalians.
George Michael was born in England but his father was from Patriki, which is now in Northern Cyprus.
I went to a live tennis match where Justine Henin advanced to the finals. I had a serious girl crush on her. I actually went to another match, because she was in the group of participants. Sadly, she was out in the first round. Ran into a buzzsaw named Serena.
Novelist Nadifa Mohamed now lives in the UK, but she was born in Hargeisa, which is now in Somaliland. She’s not exactly a household name. I read one of her novels, Black Mamba Boy, a couple of years ago, but I still had to look up her name.
My choice would be Duke Fakir, member of the Four Tops, whose father was born in Bangladesh, since I consider the Four Tops to be the greatest musical group ever.
Speaking of Belgium, you left out the most impactful Belgian of all time: Adolphe Sax.
Pierre De Geyter composed the music for the “Internationale.”
Unfortunately, he did not compose it on a saxophone.
I’d nominate Joan Armatrading as the most famous living Kittitian,
The late Eusebio (1942-2014) is probably a Top-5 all-time soccer player. He was born and lived in Mozambique until he moved to Portugal to play for Benfica at age 18.
I was going to add that one. Another SF writer, albeit less famous, is Algis Budrys, who is from Lithuania.
If you’re willing to go far back enough in history, Gautama Buddha is commonly considered to have been born in 623BC in Lumbini which is located nowadays in modern Nepal.
Well, color me surprised. I always thought that Buddha was from India. I guess what’s now Nepal might have been part of India back then.
Gernsback himself was born in Luxembourg and didn’t emigrate to the U.S. until he was 19 or 20. The only famous current person in entertainment from Luxembourg is Vicky Krieps. Wikipedia lists the following people as having some ancestors from Luxembourg: Chris Evert, Dennis Hastert, Loretta Young, and Alex Wagner (and no, she’s no relation).