I always assumed it was a "Bite the Wax Tadpole" kind of name. Sony is a Japanese company, so maybe they thought the name Vegas conveyed prestige or excitement? Maybe the sound in Japanese didn't translate well?
jdw, originally it was just called "Vegas" and did only audio. It wasn't until version 2 came out with optional video capabilities that there was "Vegas Audio" and "Vegas Video".
When version 3 arrived only "Vegas Video 3" was released with the promise that there would soon be an audio-only version, but "Vegas Audio 3" never arrived. Starting with version 4 the name went back to just "Vegas" and there has never been an audio-only version since. Strangely enough that didn't stop a lot of folks from referring to it as "Vegas Video" or "VV" right up to the present day.