Here is a gallery of customizable items in Animal Crossing New Horizons. All of these items can be customized with a custom design pattern. The list below is ordered alphabetically.
You can also view custom designs made especially for these items by browsing their specific tags or category:
Beach Towel Blue Corner Bunk Bed Changing Room Clothesline Clothesline Pole Cushion Digital Scale Director’s Chair DJ’s Turntable Doghouse Drinks Machine Drum Set Effects Rack Electric Guitar Floor Lamp Floor Seat Frozen Bed Futon Giant Teddy Bear Hammock Iron Hanger Stand Ironing Board Ironwood Bed Kimono Stand Kotatsu Loft Bed with Desk Log Bed Log Chair Log Decorative Shelves Log Dining Table Long Extra-Long Sofa Log Garden Lounge Log Round Table Loom Low Screen Magazine Rack Mama Bear Neutral Corner Outdoor Bench Outdoor Table Papa Bear Paper Lantern Pet Bed Pile of Zen Cushions Plain Wooden Shop Sign Poolside Bed Record Box Red Corner Refrigerator Retro Gas Pump Rock Guitar Scattered Papers Simple Panel Stall Standard Umbrella Stand Table with Cloth Upright Locker Vintage TV tray Wedding Welcome Board Wheelchair Wooden Double Bed Wooden Mini Table Wooden Simple Bed Wooden Table Writing Chair Zen Cushion
Partial source of information is from the Animal Crossing Wiki. Images are from Nookazon.