Are city-states like Monaco, Luxembourg, Vatican City, or Singapore not count? Singapore was a city before it became a country after all. Likewise, Djibouti was a city before there was a Djibouti country. I haven't checked but I'd imagine Guinea-Bissau is similar.
Thanks for noting this. I've included in the instructions a caveat saying that city-states are not included. After all, they "didn't give name" to the country. They just "are" the country.
I'm not sure that Djibouti counts as a city state, given that there are ten cities in Djibouti. The nation of Djibouti is 23,200 km2. That would be a huge city, covering an area 19 times greater than the combined five boroughs of New York City, but only 1/10th its population. Djibouti would need a population over 10 million before you could argue that the country is a single metropolitan area.
Thanks for your comments Kahikatea! Zimbabwe should have been definitely there. I'm adding Guinea-Bissau for completeness, but I'm not as sure about his one. Iraq I'm going to keep out of this test. The Uruk etymology is just one theory, and not even the most popular among scholars.
I can't prove it, but I believe British Honduras was named Belize in 1973 after Belize City (formerly Belize Town), which had been the capital of the colony for centuries. 'historians often say that "the capital was the colony", because the center of British control was here.' https://en.wikipedia.org/wiki/Belize_City#History
Thanks to everyone for their contributions. I'm including all of them except for Belize (unclear etymology; I've not been able to find any reputable source claiming the name comes from a city) and Tanzania (Zanzibar city is takes its name from the region of Zanzibar).
I can't prove it, but I believe British Honduras was named Belize in 1973 after Belize City (formerly Belize Town), which had been the capital of the colony for centuries. 'historians often say that "the capital was the colony", because the center of British control was here.' https://en.wikipedia.org/wiki/Belize_City#History