What's the word for the "back arm" if there is one?

Solution 1:

In anatomy, it is called the arm. “The term forearm is used in anatomy to distinguish it from the arm, a word which is most often used to describe the entire appendage of the upper limb, but in anatomy, technically, it means only the region of the upper arm, whereas the lower ‘arm’ is called the forearm.”¹

Otherwise, the term used by many people is the upper arm:
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Solution 2:

Dorland's Illustrated Medical Dictionary defines brachium as:

The part of the upper limb from shoulder to elbow.

But as MetaEd states, it is also known as the upper arm or just arm.