The domain Google.com was registered on September 15, 1997. But before that, founders Larry Page and Sergey Brin had another name for their search engine: They called it BackRub.
From Google's company history:
1996: Larry and Sergey begin collaborating on a search engine called BackRub. BackRub operates on Stanford servers for more than a year—eventually taking up too much bandwidth.
You can read more about Google and the evolution of its logo below.