I always wondered if there was any relationship (nomenclature-wise) between Kenya and a leading figure in this country’s post-independence politics, Jomo Kenyatta. I never looked it up (although this would admittedly not be a big thing), but I suppose no. Maybe it’s the other way round - the country honored him by allowing him to use the country’s name as an honorific name, very much like Mustafa Kemal Atatürk and Turkey.
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…but before modern times the Chinese did refer to themselves by the name of the Dynasty. “Zhong Guo” is a fairly modern innovation.
It is possible that “China” (coined by the Romans I believe) came from Qin, but “Qin” is not a person, it was the name of the dynasty, which in turn was the name of one of the warring states that eventually conqurered the others during that period. That name is geographical, and MAY have originated with a person from the very distant past, but the name of the first Qin emperor was Ying Zheng, “Shi Huang Di” simply means “the first emperor” and was his title. The Chinese system of names and titles is rather complex, more so when dealing with Royalty and even more so when dealing with names from 2000 years ago when the language was quite different than it is today.
The way politics in the US is going, perhaps we should rename ourselves Bush-Clinton-Bush-Clinton-…
Jomo Kenyatta named himself after Kenya, not the other way around. His birth name was Kamau wa Ngengi, and he was known as Johnstone Kamau until publishing Facing Mt. Kenya in 1938 undet the name Jomo Kenyatta. “Kenyatta” means “Light of Kenya” in Swahili.
Kenya itself is named after Mt. Kenya, a corruption of the Kikuyu name Kirinyaga or Kerenyaga, meaning ‘mountain of whiteness.’
The Greeks (ΕΛΛΗΝΕΣ) are the descendants of the ΕΛ who came from Sirius 10,000 years ago. The ΕΛ are few in numbers today but they have formed the apocryphal Epsilon Team and they have Tesla-technology weapons. In 2011 the Epsilon Team will emerge and once again the ΕΛ will rule the world.
Buy the books here: http://www.liako.gr/index.jsp 
A tiny nitpick: the country is spelled Colombia with an ‘o.’
Kamau (wa Ngengi, sometimes cited without the particle, is a patronymic) ran away to a mission at age 12, seeking an education and a broader life than the Kikuyu way of life of that day. He chose “Johnstone Kamau” as a baptismal name, and like many renamings-at-baptism, that was considered his legal name until he formally changed it to Kenyatta after the success of the book (for which he adopted J.K. as a pen name). I believe he intentionally did so in seeking a Washington/Bolivar/de Gaulle sort of role as the person instrumental in shaping the new country – though that’s a matter of psychological hypothesis, not something provable in a GQ sort of way.
I always suspected that was the way it went. Interesting to learn that it did.
Isn’t the “mountain of whiteness” in Colombia? 
Also the two Carolinas, named after King Charles I.
Well, it does refer to “snow,” but in a different sense.
The form “Colombia” is itself interesting, since Columbus is called Cristóbal Colón in Spanish. Obviously “Colonia,” meaning colony, would not be a suitable name for an independent country. The name is thus derived from the original Italian form, Colombo.
And while we’re at it, there’s also San Salvador, “Holy Savior”. Also Jesus, of course.
Acording to Thomas Bulfinch, Great Britain may be named after someone named Britto, or someone named Brutus. Bulfinch also suggests that France, Rome, and Germany were named after Britto’s brothers:
Thomas Bulfinch, Bulfinch’s Mythology, pp. 378-79 (New York: Avenel Books, 1979).
As long as Vancouver was mentioned, what about Alberta…for Prince Albert?
As well as Prince Edward Island, named after Queen Victoria’s father.
Doing states and provinces:
Prince Edward Island – named after Queen Victoria’s father, Prince Edward Augustus, Duke of Kent
New Brunswick is not eligible. It was, according to two apparently reputable websites, named after (1) the city of Braunschweig, capital of the Kingdom of Hanover, or (2) the House of Braunschweig-Lunenburg, AKA the House of Hanover – in either case paying tribute to the British royal house between 1714 and 1837, under its Anglicized form Brunswick.
New York – named after King James II of England, its first Protector after its being conquered from the Dutch and at that time Duke of York.
Pennsylvania – after named either William Penn, or named by him after his father
British Columbia – after Christopher, this time without the second “o”
It’s worth noting that the two halves into which the Kingdom of Saxony was divided for several decades in early modern times were officially distinguished by the German equivalents to “Ernestine” and “Albertine” (and I don’t have the German forms at ready reference, but seem to remember they used -liche as the appropriate suffix) after the two heirs between whom the kingdom was divided: * Konigsreich von Sachsen Albrechtenliche* or something of the sort being the official usage when the distinction needed to be drawn.
Don’t forget the country founded by Larry United Kingdom of Great Britain and Northern Ireland. It’s called Larryland.
Bulfinch is… a mythologist. It’s a lovely myth, but has about zero likelyhood of being true. Romulus is also rejected by most people as anything but a fictional person, made up to be the ancestor of the Romans and named accordingly. So ‘Rome’ came before ‘Romulus’.
Especially since the Persians themselves called (and still call) their country not “Persia” but “Iran”. (“Pars” or “Fars” is the name of a province within Iran, though.) The name “Iran” is derived from a cognate of “Aryan”, but that’s the name of a people, not an individual person.
From Australia, three states would be included:
Tasmania: as already noted by **glee ** and Giles, named for the Dutchman Abel Tasman
Victoria: named for Queen Victoria
Queensland: named for Queen Victoria
The Cook Islands, named after James Cook, the English discoverer.
Note that part of the Wikipedia article contains clear errors. Cook could not have visited in 1813 as he was killed in 1779 on a beach in the Sandwich Islands.
Other Pacific nations such as Marshall Islands and Northern Mariana Islands could also qualify as answers to the OP.