Why is the part of the hair and part of the brain both called the medulla?

Because medulla means the middle or interior part of something. With regard to hair, the medulla of a piece of hair is the innermost layer of the hair shaft; with regard to the brain, the full term is the medulla oblongata, which is often shortened to just medulla when it's clear that the reference is to the brain, and I think the term is used in this instance to mean the first part of the brain, between the spinal cord and the rest of the brain.