I wanted to exclude America because the naming was somewhat random anyway and because it kind of overshadows everything.
Well, what about Asia? Does being named after a band count?
San Bernardino County, CA, LARGEST in the U.S., (20,000+ sq. miles) named after Saint Bernardino.
Alaska, over 500,000 sq. miles, has some boroughs of large sq. mile areas named after people.
What about Columbia? (Not Colombia)
Also, how many different places are named Washington?
Saudi Arabia, named after Abdul-Aziz bin Saud.
Vespucci got the nod over Columbus because he was the first or among the first to propose that the discoveries were actually a new continent, rather than part of Asia as Columbus insisted, so I wouldn’t consider it random.
In any case, I agree that if the Americas/United States of America, China, and India are excluded, the winner is the Philippines.
Why not Colombia? It’s also named after Columbus (Cristobal Colon in Spanish). Colombia has 10 times the population of British Columbia and many times the population of the District of Columbia.
Columbia has a grander meaning than that as well, more or less synonymous with ‘America’.
But is Colombia bigger than Bolivia?
Much bigger, with a population of 47 million vs Bolivia’s 10 million.
Nice.
When was that India’s official name?
Right now. Bharat Ganrajya is the official name of what we call the Republic of India in English.
Washington State, Washington, DC
Bolivia (Simon Bolivar)
Rhodesia (Cecil Rhodes), now Zimbabwe
For those who think America (North and South) counts towards this OP: The combined population of the Americas is 934,611,000. 
Columbus was a Latinized name too (Italian, Colombo). So was Confucius (from K’ung Fu-tzu, or any of a variety of romanized variations given in Wikipedia).
Even the most skeptical theologians, guys who don’t believe Jesus existed, are certain that St. Paul was real- indeed, more than a few of them think Paul made up Christianity.
Paul NEVER appears in the Gospels. He became a Christian long after the death of Jesus. The letters he wrote are the epistles that appear in the Bible.
At its height, Rome was a significant portion of the world.
I think Colombia with 47 million may be the winner.
I had a look at Chinese provincialand Indian state name etymologies, in the off chance one of those qualified. None of the chinese provinces were named after people, and Jammuin India only has 13 million.
Yes, but “Romulus” was a mythical figure named after the city, in the same way that “Britannia” is a consciously mythical personification of Britain.
There never was a guy named Romulus who founded a city and it was named after him. There was a city named Roma and they figured the city had to be named after someone, so they invented Romulus and made up stories about him and what a badass he was. Like that time he totally killed his brother for hopping over the city wall and being a jerk about it.