Not a teacher.
Without a door, I would call it a shelf. I might also refer to the entire piece of furniture as "the shelves." A set of shelves that is used primarily for books is a bookshelf or a bookcase, depending on your preference.
I store my clothes in a dresser. My dresser is a combination of a cupboard with shelves and drawers. I also have a closet, which is the area of my room that I use to hang clothes and store things.
As for a furniture word bank with pictures, maybe you can just go to an English furniture store's website. They will have pictures of their products with descriptions that include their functions (dressers, drawers, shelves, cupboards, cabinets, couches, loveseats, armoires, recliners, hutches, etc.).
I don't know how many kinds of furniture names you know, so I put a bunch of stuff just in case. Sometimes, the different types overlap. My picture of a hutch contains drawers and cupboards (or cabinets, depending on what you want to call them. They might be different, but my area uses them pretty much interchangeably) with shelves inside.
I hope I was helpful.
Student or Learner