This answer from a ways back by u/lukemacu has some relevant history around operation code names.

Specifically in the US case, Just Cause for the 1989 invasion of Panama is the first example of the modern "marketing" style of operation code name. This developed from the 1975 introduction of the computerized Code Word, Nickname, and Exercise Term System (itself shortened to NICKA). Using this unified system as a common database, the Joint Chiefs of Staff assigned 24 different Department of Defense components, agencies and commands a series of two alphabetical letters to use the assigned component's/command's staff then use the letters to generate operation names. In 1983 US Atlantic Command had UR as one of its codes, and therefore chose "Urgent Fury" for its operation name for the 1983 invasion of Grenada. But this was something of an outlier (and it was mocked in the US press), and it should be contrasted with operation names like Eldorado Canyon for the 1986 airstrikes against Libya, Praying Mantis for 1988 air strikes targeting Iranian assets, and Golden Pheasant, also in 1988 for operations directed against Nicaragua.

The change that started with Panama came at the urging of US Army Lieutenant General Thomas W. Kelly, who was in charge of the Pentagon's National Military Command Center (which handled press briefings), and who had a degree in journalism. This was at the urging of General James J. Lindsay, Commander in Chief of Special Operations command, who reputedly told Kelly: "Do you want your grandchildren to say you were in Blue Spoon?" Kelly worked on alternatives with another general and they finally hit on "Just Cause", and the trend started from there, continuing with Desert Shield the following year, and Desert Storm the year after.

Another notable change that happened at this time is that operation codenames took on much larger roles than they had previously, when an operation was just that - a particular plan for a particular action within a larger war (Operation Overlord being a few weeks' of a campaign in Northern France in 1944, or Operation Cedar Falls being a three-week search and destroy mission in Vietnam in 1967). Starting with Desert Shield, operation names became much more broadly encompassing, often denoting an entire conflict, and not just a single operational action within it, assuming the two were even indistinguishable. So for example "Desert Storm" itself became a shorthand for the whole war against Iraq in 1991, which in some ways is a bit confusing in that the air campaign, the Battle of Khafji, and the ground offensive technically were all very different things in that one operation, and that in an earlier era might have been labeled distinctly (which did get other branded names, although these are less well-known: the ground offensive was Desert Saber, the redeployment out of theater was Desert Farewell, the distribution of postwar aid was Desert Share, etc.).

Naming US military operations very much has been a branding exercise since, and this very much as an eye towards public relations, often relying directly on media coverage for feedback - a 1991 relief effort in Bangladesh was originally named Operation Productive Effort, but Colin Powell disliked it, and the operation was renamed Operation Sea Angel based off of coverage of the already-underway operation. The US military has gotten much savvier since then about what sort of message it wants to convey to the public with operation names, and how well names are received by the media.