Wikipedia has more about the origins of the name Google:
The Goo-Goo song --> the Google in Googleland --> Mr. Google
--> Googol the number --> Google the search enginehttp://en.wikipedia.org/wiki/Barney_Google
The OED will tell you more about the goo-goo eyes, and
"the googlies that do not google" (in cricket).
As to the suggestion by ilyena, this may be to "goo-goo", as in the example OED gives from Mark Twain,
"The duke ...just went a goo-gooing around, happy and satisfied."