Google explains the name at the bottom of this page:
http://www.google.com/corporate/index.html

That says: What's a Google?

"Googol" is the mathematical term for a 1 followed by
100 zeros. The term was coined by Milton Sirotta, nephew of American
mathematician Edward Kasner, and was popularized in the book,
"Mathematics and the Imagination" by Kasner and James Newman.

I remember reading, many years ago, that John von Neumann was talking
with his son or nephew or grandson about big numbers and asked the kid
what they should call a 1 with a hundred zeroes after it. The kid
thought a moment and said, "googol."

Is my memory playing a trick on me?

vince