Full name match between files

Hi folks, I've got a scenario I need help with. I've got an Excel file containing names, last names in column C and first names in column D. I've got another file containing a different list of names in the same format. What I want to do is check if the full names in file 2 match any of the full names in file 1.

Here's an example:

File 1:
DOE | JOHN |
DOE | JANE |

File 2:
DOE | JOHN | MATCH
DOE | ANDY |

I'm looking for a formula that will see if the values in that row of column C and D in file 2 match any rows in column C and D of file 1. So if there's a JOHN DOE in file 1, the formula will return "MATCH" or some confirmation that the names are in both lists, and return blank if the full name isn't in file 1. I tried all kinds of combinations of VLOOKUP, EXACT, FIND, MATCH, AND, IF, and ISNA, but the best I've come up with is two separate lookups and a check if both matched. The problem with that is that if I'm looking for JOHN DOE and there's someone with the last name of DOE and the first name of JOHN, the check will return true even if the matches aren't in adjacent cels in the same row. Any help would be greatly appreciated. Thanks!