In case you want to do an Array check, this formula might be what you are looking for
=IF(COUNTIFS($A$2:$A$7,$A2,$B$2:$B$7,$B2)=1,"New",IF($C2=SMALL(IF(($A$2:$A$7=$A2)*($B$2:$B$7=$B2),$C$2:$C$7),1),"New","Repeat"))
Use it on D2 and drag it down.
Note that this is an Array formula, so when you edit / enter it, you will need to hold Ctrl-Shift and hit Enter. If you see the formula being wrapped inside a { } then you did it right.
This formula will flag "New" if a customer only appears once in a month. In case a customer appears more than once, it will flag "New" to the most recent date of the order, and "Repeat" to the rest.
Note that in case that same customer has two orders in the most recent date, both row will be flagged as "New"
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