Matching Data with multiple columns

In your example, you get NA only because "bill" is not in Column A. Would you also want NA if D7 was "mike" and E7 was "orange"? Either way, I would simply test for those condition in the "FALSE" part of the formula.
This formula tests only for Column A, but it's easy enough to add a test for Column B.

=IF(ISNA(VLOOKUP(K3,$J$3:$J$31,1,FALSE)),IF(ISNA(VLOOKUP(D3,$A$3:$A$31,1,FALSE)),"N/A","FALSE"),"TRUE")