An excerpt from The Jargon File:
Some people are confused over whether this word is appropriately ‘UNIX’ or ‘Unix’; both forms are common, and used interchangeably. Dennis Ritchie says that the ‘UNIX’ spelling originally happened in CACM's 1974 paper The UNIX Time-Sharing System because “we had a new typesetter and troff had just been invented and we were intoxicated by being able to produce small caps.” Later, dmr tried to get the spelling changed to ‘Unix’ in a couple of Bell Labs papers, on the grounds that the word is not acronymic. He failed, and eventually (his words) “wimped out” on the issue. So, while the trademark today is ‘UNIX’, both capitalizations are grounded in ancient usage; the Jargon File uses ‘Unix’ in deference to dmr's wishes.