How to refer to the piece of furniture that bars use to store their drinks?

Solution 1:

I believe that's called the back bar, a generic term referring to the hutch, cabinets, shelves, etc., behind where the bartender stands.

Here's a screen shot from a store that sells bar furniture:

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Note: Example used for illustrative purposes only.  I am not trying to promote the website.

Solution 2:

Use "shelves". That's the word that would come naturally to me.

Solution 3:

I thought that was called a bar. When you see an "antique bar" sold, it is often the piece that houses the liquor, not the counter where the patrons sit.