Do you have a tape measure? Measure 18”” of the rod in your current closet. Is that wide enough? Measure front to back 20”” and see if a hanger with a dress or a coat would fit in that 20”.

My Ikea hangers would fit, depth-wise.

Plus you could use some space savers to increase what you can store like these

Or you could go wider instead of deeper. This wardrobe is 19.5"w x 15.5"d

I mean, yes, it is very small, but still technically a closet right?

Do you need to have it specified as a bedroom? If not, why not just get an armoire?

Why are you interested in making the smallest possible closet? Do you desperately need that space elsewhere?

I'm not usually one to harp about resale, but I would not want to buy a house that did not have a useful closet in a bedroom. Even your own needs might change - we had a nephew live with us for a summer, so our spare bedroom was fully occupied for 3 months.

If you are building or remodeling, please check your building codes. In most places in the U.S., you can't call it a bedroom if there isn't a closet. Your building codes may specify minimal dimensions. 24 inches is the standard depth to fit most hangers. 18-20 inches wide was ok in the early 1900's. I've lived with these, and it was unpleasant. By the 1950's closets were usually 36-48 inches wide. That's small by current standards, but usable with good space planning. That's the absolute smallest I would use. 60-72 inches would be better. Down the road, if someone wants to use it as a bedroom, you can be certain that the occupant won't want to go to other parts of the house for clothing.

Build in/attach/trim in Ikea wardrobes and you got yourself a closett