It’s Aliki, the wedding planner speaking!
In order to make your research for accommodation easier, I gathered some information that could be useful to you, concerning hotel contact details. All hotels listed are located in Agia Anna & Agios Prokopios, however there are more options both in Agia Anna and in the nearby villages of Agios Prokopios and Plaka, as well as chora (town) of Naxos.
The couple has booked their accommodation on Ktima Lino Hotel https://www.linonaxos.com/
Iria Beach Art Hotel (Agia Anna) email@example.com 22850 42600
Kouros Art Hotel (Stelida) firstname.lastname@example.org 22850 29150 / 693 462 1184
Athina Studios & Suites (Plaka) email@example.com 697 8334290 / 22850 41153-4
Studios Elli (Agia Anna) firstname.lastname@example.org 697 2871772
Hotel Artemis (Agia Anna) email@example.com 697 8334290 / 22850 41150
Studios Aspasia (Agia Anna) firstname.lastname@example.org 697 3666068 / 22850 42507
Studios Eirini (Agia Anna) email@example.com 697 6352410 / 22850 41947
Studios Despoina (Agia Anna) 22850 42009 / 22850 42190
Studios Litsa (Agia Anna) 698 1814681
Pansion Elena (Agia Anna) firstname.lastname@example.org 693 2416239
Althea Hotel (Agia Anna) email@example.com 693 2416239
Hotel Anemomilos (Agia Anna) firstname.lastname@example.org 697 3032199
Hotel Summer Dream 2 (Agia Anna) email@example.com 694 7222388
Hotel Perla (Agios Prokopios) firstname.lastname@example.org 697 6352410
This list consists of hotels where you can have special rates for really valuable rooms, just mentioning that you are guests of the wedding hosted by “Banana beach bar” (owner Maria Korres) on the 10th of September.
By the time you make your reservation please send your accommodation details (hotel, number of guests, duration of your stay) on applesandmints&gmail.com
Special note: Please keep in mind that on sites like booking.com you might find similar rates but in that case the room type (location on the hotel, size, renovated or not etc) might be different.