I couldn't find any baptisms in Hampshire for Ellen/Eleanor.
Purkis is a good Hampshire name, as testified by the story of the death of William Rufus. Purkis, a charcoal burner, put the body on the back of his cart and took it to Winchester, so the story goes.
https://archaeology-travel.com/engla...est-hampshire/
Timber provided the livelihood for many generations of Purkises and New Forest dwellers. Many became sawyers and carpenters and many plied their trade in the naval dockyards at Portsmouth.