The minimum number of moves is
6 with a slanted letter or 7 without
MLXVI in roman numerals.
1066 has 11 matches - and so does that so:
Taking either 6 or 7 moves.
This is the minimum because
'ONE' only shares 5 matchsticks in common with 'MLXVI'(slanted V version) - meaning that the other 6 have to be moved. Therefore 6 is the minimum. Here is a diagram:
You can see there are only 5 matchsticks (black) that are shared - and the other 6 green matchsticks have to be moved to red.
PREVIOUS - Thanks HughMeyer for suggesting moving the overlay to the left for less moves
I previously thought it was 8: