Last week the Iraqi capital of Baghdad fell in a statue-toppling ceremony that reminded many of the Soviet satellites of Eastern Europe pulling down their statues of Lenin. On Monday at the Pentagon, Maj. Gen. Stanley McChrystal said, “I would anticipate that the major combat engagements are over.” Saddam Hussein’s purported “last stand” in his home city of Tikrit was more of a “last sit and surrender,” in part because there was no Saddam to take a stand there.

The regime is noted in news articles now as an “ex-regime” or “former regime.” So, for all intents and purposes, the “war” is over and the focus shifts to filling the resulting hole with something resembling a political system.

The “war” is over. What war? More precisely, what is or will be the proper terminology for the conflict that lasted from approximately March 19 to April 9, 2003 — a conflict that began and ended within nearly the same span of the NCAA men’s basketball tournament?

Picking a name for this one should be straightforward, shouldn’t it? But the press had a hard time naming the first conflict in the Persian Gulf region. The official military name for the operations were “Operation Desert Shield” when the troops were massing in Saudi Arabia and “Operation Desert Storm” when the ground war began. But no one writes operations in the history books. At the most, they are called campaigns, parts of a larger war. And so the press often used “gulf war,” in lowercase, but many had settled on “Persian Gulf War.”

Even the simple terminology like that is loaded, calling this undeclared action a “war.” According to the Constitution, only Congress can declare war, and the last time a formal declaration was issued, it was against Japan, Germany and Italy in December 1941. The “Korean War” was a police action that still technically has no peace treaty. The “Vietnam War” was another police action.

There are those who will have no part in incorporating the title of this military operation into the permanent name. The Des Moines Register was criticized in a letter for running the phrase “Operation Iraqi Freedom” across the top of its pages because it was Bush administration “propaganda.” On the other hand, some abstain from “Civil War” or “War Between the States” in favor of less-neutral titles like “War of Southern Independence” or “War of Northern Aggression.” But even then, those are not the generally accepted or historically printed titles.

Should we name it after the opponent? We have the French and Indian War, the Mexican War and the Spanish-American War. Perhaps this could be called the Iraqi-American War.

Or, reaching farther back, should we name it after a leader? In 1675, a chief of the Wampanoag tribe, Metacomet, united other tribes to fight against British settlers. The settlers referred to him as Philip, and so we have King Philip’s War.

So would this be President Bush’s War? There are a lot of anti-war protesters who would agree with that. Their apparent hatred of not just the war, but the president himself, wouldn’t make them disagree. But that title would not be accurate because it discounts all those in the administration who weighed in beforehand about the decision. Remember, Congress is also a party, having given approval for use of force earlier.

The decision about this conflict has already been made once in two publications. USA Today’s March 20 headline used the phrase “second Gulf War,” much like one can say “second world war” (caps optional), while the March 31 cover of Time used Roman numerals for “Gulf War II.”

Author Tom Clancy, in the fiction book “Debt of Honor,” wrote of a Second Persian Gulf War that involved U.S. forces going against a united Iran-Iraq army. Is that title accurate for the real-life operation? The previous war had a lot more action on the gulf itself, while this was a land war with ships in both the Persian Gulf and the Mediterranean Sea.

But because the conflicts in 1991 and 2003 are connected so closely, it will be accurate to write this off as either Gulf War II, or the Second (Persian) Gulf War, placed in the encyclopedia under G.

It’s unfortunate that one must even consider terminology for a sequel so soon after the original. After all, World War I remained the “Great War” for more than 20 years. Unlike Josh Hartnett’s anachronistic, banal line in “Pearl Harbor” — “I think World War II just started” — we knew this one was coming beforehand. It is for that reason that this short war is already looking for its historical title.