Got it! This site says that the original name was Desert Shield when the operation started on Aug. 7, 1990, and the name changed to Desert Storm when the air war began on Jan. 17, 1991.

I think the only thing that really matters to the military is the designation DS. They probably use this on their paperwork for accounting purposes. The mnemonics Desert Storm and Desert Shield were chosen strictly for PR purposes, and as such, were easily changeable.