One way to do this is using the COUNTIF() formula. Supposing your
names in both Sheet1 and Sheet2 are in column A, I wrote this formula
in Sheet1 cell B1:
=COUNTIF(Sheet2!A:A,A1)

This will return the *number* of times that the name in Sheet1 appears
in Sheet2. Is that of any use? It's more informative than "OK" and
"NO" responses. If you need the OK and NO then use this formula:
=IF(COUNTIF(Sheet2!A:A,A1)0,"OK","NO")

A caveat: If "Sam Spade" appears in Sheet1 and "Samuel Spade" appears
in Sheet2, no match will be found. Similarly, "Ed Bagley, Jr." will
not be matched to "Ed Bagley Jr" because of the punctuation difference.