Try this:
A2: =IF(SUMPRODUCT(--(A2&B2=$A$2:A2&$B$2:B2))1,"Duplicate","")
A3: copy down

Ola Sandstrom

Note:
The & joins the First&Lastname.
-- is a trick to turn True into 1 and False into 0, so they can be added.
The 2nd time a Names comes up will be called a duplicate due to the $A$2 and
$B$2. If it should be the opposite (the last name is the most current
address) 'fix' the last cell ($A$500$ and $B$500$) instead of the first cell
($A$2 and $B$2).

You can also use the formula in combination with Conditional formatting :
Formula is =... to highlight new duplicates as they are entered.