Just to clarify, Siri Inc. is the company that Apple acquired in April of 2010. Siri Inc. developed Siri, a personal assistant application that was available for awhile on Apple's App Store before the acquisition. After integrating it into the 4S, Apple retained its original name rather than rebrand it.

As a startup, when coming up with Siri's name, they wanted something that was easy to remember, short to type, comfortable to pronounce, and a not-too-common human name. And they were able to get the domain name for not too much money...

Once Siri became the leading candidate, everyone on the team had their own favorite explanation of the meaning. The name Siri is of Scandinavian origin and the meaning of Siri is "beautiful victory".

The fact that Siri was unveiled to the world with the iPhone4'S' may also have had some weight in the decision to retain the Siri name. i.e. There's the iPhone 4, then there's the iPhone4S - which would people most commonly associate with Apple's brilliant new Siri voice recognition assistant?