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Google does not answer everything. Consider:
""Wilson"" 204.000.000
""George W. Bush"" 47.500.000 - ""Bush"" 302.000.000
""Winston Churchill"" 9.650.000 - ""Churchill"" 34.600.000
So what is the more common name?
Not counting in each case that of course any hit for ""Thomas Woodrow Wilson"" will be included in ""Woodrow Wilson"" too.
I can respect disagreement but not silly and lazy pseudo-arguments like a google search. 
Since Grover Cleveland has been used as an example: Grover was one of his first names, whereas Woodrow is Wilson's mother's maiden name. (talk) "