Sure, the Wikipedia entry lists a number of different names:
The war is also known under other names, such as the Persian Gulf War, First Gulf War, Gulf War I, Kuwait War, First Iraq War, or Iraq War before the term "Iraq War" became identified instead with the 2003 Iraq War
The point is the 2003 coalition invasion isn't referred to as the First Iraq War; if using that term, it's commonly understood to mean the events of 1991. I could have phrased it better as "What's commonly referred to by the first Iraq War would be following the invasion of Kuwait in 1990."
The war is also known under other names, such as the Persian Gulf War, First Gulf War, Gulf War I, Kuwait War, First Iraq War, or Iraq War before the term "Iraq War" became identified instead with the 2003 Iraq War
The point is the 2003 coalition invasion isn't referred to as the First Iraq War; if using that term, it's commonly understood to mean the events of 1991. I could have phrased it better as "What's commonly referred to by the first Iraq War would be following the invasion of Kuwait in 1990."