The official name of Facebook in China, as it appears on the Chinese version of its Website, is simply "Facebook." It is unofficially, but commonly, referred to as Liǎnshū 臉書 (lit., "face book").
Lately, however, Fēisǐbùkě 非死不可 has become a popular way of transcribing the name "Facebook."
And what does Fēisǐbùkě mean? "Absolutely must die." Fēi means "not," sǐ means "die," and bùkě "impermissible, cannot." In other words, Fēisǐbùkě may be rendered as "cannot not die" (double negative), i.e., "absolutely must die."
Although this is a very clever transcription, it — and all other Facebook name games in China — amount to no more than a hill of beans. Facebook is usually blocked in China (as it is in Pakistan, Iran, and Syria; does North Korea have an Internet?), so I suppose it doesn't really matter much what people call it. No matter how they refer to Facebook in China, they can't use it. The government of China is undoubtedly pleased with the Fēisǐbùkě ("Absolutely Must Die") moniker.
[A tip of the hat to Tansen Sen]