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My understanding is that the name "pool" refers to man-made modifications to a river, and references to "Underbarrow Pool", Helsington Pool, and Rusland Pool (in a completely different valley further west), refer to sections of river that have been raised and embanked to prevent surface water from adjacent high ground flooding the valley floor. References to "River Pool" imply a misunderstanding of the use of the word "pool" in this way. I have seen a reference to this river as "River Poole" dated 1839. Locally the upper section of this river is known as Chapel Beck, and Underbarrow Beck lower down.