Skynet not Terminator
Lets just be clear here - Skynet is the series of MoD Satcom platforms that dates right back to the early 1970's - way, way before Arnie got into his Terminator suite. Apparently the film makers were looking for a nifty name and thought that they had come up with one that no-one had every thought of, only realising their mistake after the film was released and someone pointed this out to them!
Also Skynet was the first military satcom system; up until it was launched everyone (i.e. the Americans) had been saying that the military had no need for satcom. Skynet-1 was so successful that the critics shut up immediately - the rest, as they say, is history.