What are the names of all of the operations that have taken place
during the war in Iraq?

Hello veryvermilion-ga,
I believe you'll find all the information on US military operation
names in Iraq in this page:

Global Security.Org - US Military Operations
http://www.globalsecurity.org/military/ops/swa-ops.htm

To show some examples, I will list significant operations, mainly
those during the 1991 Gulf war and the 2003 Iraq Invasion:


Gulf War Era:

Desert Shield 
From 02 Aug 1990 to 17 Jan 1991

Imminent Thunder 
From Nov 1990 to Nov 1990

Proven Force 
From 17 Jan 1991 to 28 Feb 1991

DESERT STORM 
From 17 Jan 1991 to 28 Feb 1991

Desert Sting
From 29 Jan 1991 to 29 Jan 1991

DESERT SWORD / DESERT SABRE
From 24 Feb 1991 to 28 Feb 1991

Positive Force
From Summer 1991 To Summer 1991

Desert Calm
From 01 Mar 1991 to 01 Jan 1992

Desert Farewell 
From 01 Jan 1992 to ?? 1992


2003 Iraq Invasion:

IRAQI FREEDOM
Major Combat Operations
From 19 Mar 2003 to 01 May 2003 
Occupation / Reconstruction
From 01 May 2003 to Present	

Southern Focus 	
From Jun 2002 to 19 Mar 2003
Desert Shift (in Saudi Arabia) 
From Nov 2000 to Dec 2003

As of this time, Iraqi Freedom is still ongoing in the
Occupation/Reconstruction stage.

For information on other operations, look at these pages:

Global War on Terrorism / GWOT (Including Enduring Freedom in Afghanistan)
http://www.globalsecurity.org/military/ops/terror-ops.htm

Completed Post Cold War Operations
http://www.globalsecurity.org/military/ops/recent-ops.htm

Global Security Title Page of US Military Operations
http://www.globalsecurity.org/military/ops/index.html


Google Search Strategy:
I used my previous knowledge of GlobalSecurity.Org and its list of
military operations.

I hope this has been a helpful answer. If you need something
clarified, or have a problem with the answer, do please post a Request
for Clarification before rating and I'll come back to you as soon as I
can. Thank you.

Remember "Operation Infinite Justice"? I think that was the initial
name for the Iraq invasion, which had to be changed because Muslims
found it offensive (only Allah, the Infinite, can administer Justice).

Personally, I was offended by the operation itself, in which thousands
of innocents were (and continue to be) killed.

Thanks for the five-star rating!