Although there are a few agencies that can find accommodation, ferry tickets, rental cars, excursions, and lots of other things for you, it is best to contact the owners directly. You will find hundreds of apartment options of all kinds in Naxos.
Many have their own website. See also booking, Airbnb or Google Maps
There are Naxos lovers in this forum who will undoubtedly be able to give you some good addresses if you are a little more specific about what you are looking for.
You can also check here:
https://www.naxos.net/accommodation.php