Notes

My 5 cities (I knew the first two, due to that 'Istanbul song') were:

a) Constantinople -> Istanbul
b) New Amsterdam -> New York
c) York -> Toronto
d) Bombay -> Mumbai
e) Leningrad -> St. Petersburg

Tenochtitlan comes first to my mind.

Elaborating on Temaharay's list:
Byzantium â Constantinople â Istanbul
St. Petersburg â Leningrad â St. Petersburg

I might be mistaken, but I believe:
Menlo Park â Edison

I guess Edison NJ isn't exactly a major city, so even if I'm right, that probably shouldn't count.

Salisbury -> Harare

It is a national capital.

Aaaarrrgh!!!! Brain fart!

Edo â Tokyo

How in hell did I forget that?

Hot Springs -> Truth or Consequences

Again, what is major?

Saigon -> Ho Chi Minh City

Isn't this fun?

Bombay -> Mumbai doesn't count IMHO; that's more just a difference in transliteration. Same with Peking -> Beijing, or Canton -> Guangzhou. But Istanbul counts twice, as does St. Petersburg. So I only need New York to round out my list.

I was racking my brain to come up with five but was struggling. Like Nemo I discounted the ones that I thought were just changes in pronunciation. However, if that's allowed then Danzig->Gdansk (and just about every other city in Poland) counts.

Oslo => Christiania => Oslo.

Lutetia => Paris.

A few more of varying degrees of importance and differentness:

Beaverwick => Ft. Orange => Albany
Ville-Marie => Montreal
Newport, In => Fountain City
Short Creek, CO => Colorado City
Hollywood By the Sea => Hollywood

Beaverwick? That is a great name!

Seriously, why the hell would anyone want to change that?

But if you are going for smaller US cities, I submit:

Cape Canaveral >> Cape Kennedy >> Cape Canaveral

And of course, Pig's Eye >> St. Paul.

Beijing has changed its name twice in the 20th century. It was named Beijing (Northern Capitol) for many years until the Kuomintang rulers moved the capitol to Nanking in the 1920s. The name was changed to Beiping (Northern Peace). When the communists took mainland China, they moved the capitol back to Beijing and of course changed the name back again.

Closer to home:

Gastown => Vancouver, BC

Pile-of-Bones => Regina, Sask.

They should have kept the original names.

Why was it called Pile-Of-Bones????

Well, I'd like to add:

Chemnitz -> Karl-Marx-Stadt -> Chemnitz

and

Tsaritsyn -> Stalingrad -> Volgograd.

And, a rather obscure one:

Rome -> Colonia Commodiana -> Rome (very short-lived)

Oslo and Instanbul are already taken, but
Eboracum -> Jorvik -> York
Neapolis -> Neapel -> Napoli
Reval -> Tallin
Königsberg -> Kaliningrad
Smyrna -> Izmir
Ekbatana -> Korramshahr

And of course, the small fortified Swedish settlement Nöteborg was enlarged to become Petersburg :-)

Add the controversial attempt to change Pretoria to Tshwane, Republic of South Africa.

St. Petersburg -> Petrograd -> Leningrad -> St. Petersburg. The Russian form of the current name is transliterated as Sankt Peterburg.

Beijing has been known by many names. Peking is just a variant Romanization of Beijing, not really a different name. Another historical name is Peiping. And it was called Cambaluc by Marco Polo.

Bytown -> Ottawa, Canada.

Ah, South Africa! There are hundreds of cities changing their names, most with very very good reasons to do so.

@Greg: Why was it called Pile-Of-Bones????

There was a major buffalo jump there, the name was descriptive.

Pile of Bones

In 1882, the site of the future city of Regina, capital of the North-West Territories and of the province of Saskatchewan, was selected. The chosen site was the point where the route of the Canadian Pacific Railway crossed a creek variously called Pile o' Bones, Tas d'Os, Manybones, and Bone Creek. The creek finally became known as Wascana from the Cree term for bones, Oscana. A few miles downstream, where its valley is more pronounced and numerous cutbanks occur, was the "Old Crossing", a ford on the historic cart trail from Fort Qu'Appelle to Wood Mountain and Cypress Hills. In that vicinity the buffalo bones had accumulated.

The pile of bones from the Cree Indian hunts was quite a sight to the early settlers. The bones resulting from the slaughter were carefully assembled into cylindrical piles about six feet high and about 40 feet in diameter at the base, with the shin and other long bones radiating from the centre to make stable and artistic piles. During the second half of the 19th century, the Métis also slaughtered large numbers of buffalo in this area, and the creek was littered with countless bones.

Sources:
Saskatchewan History Vol. XIX.
Riddell, William A. Regina from Pile O'Bones to queen city of the plains, an illustrated history.
Burlington: Windsor Publications, 1981.

AFAIK, there was no buffalo jump near Regina.

Buffalo jumps are somewhat overrated in terms of their actual existence anyway.