Her last program held a voting pool to pick a name and ended up with "Totally Not a Laser Death Ray Facility" unfortunately coming in 2nd place.
"Star Wars" itself was the name of a previous defense program, so, I'm sure this debate was had out decades ago.
1. https://en.wikipedia.org/wiki/Strategic_Defense_Initiative#C...
https://www.copyright.gov/circs/circ33.pdf
You're probably thinking about trademarks, which only protect the use of an identifier when used in the business of a particular trade.
I mentioned in another comment that George Lucas tried to sue over people calling the SDI "Star Wars" back in 1985. I can't find any evidence now, but I believe he once sued either the Air Force or NRO (can't remember which) over a mission patch with an x-wing on it.