The first Press Release on the subject can be found at
http://www.microsoft.com/Presspass/press/2000/jun00/forumumbrellapr.mspx
It doesn't really shed any light on the subject directly, except to elucidate my first answer.
The "exact meaning of dot in dot net' is simply . ; it is how you pronounce Microsoft .NET
Being all in caps, you'd expect it to be an acronym or something similar, but I can find no references that aren't post-contrived. The Microsoft .NET Framework v1.0, which is where it all started off, was known as COM+ 2.0 and COM Object Runtime (COR) during development. My best guess is that the wags said "What do we replace COM with?" and the answer was "NET, cause ORG just won't work for us..."
But I would be pleased if someone could trump my search-Fu.