This (天网, or "sky net") most likely comes from proverb "天网恢恢疏而不漏" (tian wang hui hui shu er bu lou), meaning "Justice has long arms."

This saying was from Lao Zi, going back thousands of years.

It might be both. Like here where .gov nerdy projects will be some long name starting with "Operational" that'll make the pointy hair bosses happy, but when you look at the title and subtitle it spells out Optimus Prime. I can imagine similar games being played in Mandarin.

It also sort of looks like heavenly internet, where heavenly or celestial has a lot of associations in Chinese that resist easy translation.

I wondered whether it might just be a nickname or a case of two different Chinese words translating to the same English word, but nope, both are 天网.

Here's the Baidu Baike page on Skynet from the movie: https://baike.baidu.com/item/%E5%A4%A9%E7%BD%91/3030631

Here's a post by the Chinese government, reporting that internet users demand Skynet to reach full coverage faster: http://www.gov.cn/zhuanti/2017-03/17/content_5178139.htm

So if it's a nickname, the Chinese government has no qualms about using it.

Yikes, really makes me wonder if they are getting ideas from dystopian science fiction films as well as black mirror.

Britain put comms satellites up in 69 (to the present) called Skynet.

So hardly the first.

The Terminator was released in 1984, so it seems reasonable to rule out sci-fi as the inspiration for the British Skynet's name

It could have been the opposite (the movie was influenced by the British satellite network), however.

天网恢恢疏而不漏 pretty sure more then 99% people in China knows it. Terminator movie? 10% at most(which is crazily overestimated)

Intentional, I'm sure.