Already used, British milsats.
Name predates terminator franchise.
Name predates terminator franchise.
Don't worry. It's possible Elon will have a proper AI play some day, with a project that's more deserving of the name.
Seeing as he's concerned about safety, I can think of no better way to instill an ethos of caution into an army of AI researchers than having them show up to work at Cyberdyne Systems every day to build Skynet.
I don't think the British military have an exclusive copyright on the use of the word Skynet.