Is "Kasoinah" Really Gascoigne?

The mother of my fifth great-grandfather Abner Rea (1776-1825) is believed to have been Joannah (or Hannah) Kasoinah, wife of James Rea. She was possibly born in present-day Henry Co., VA. Some researchers believe she was Indian with fewer still claiming more particularly that the Kasoinah surname is somehow Cherokee. (Cherokee is almost a default setting for Southerners in reference to their putative Indian ancestries.) Other researchers point out that there is no real evidence for Joannah/Hannah's Indian origins.

Kasoinah is, as best I can tell, a name unique to Joannah/Hannah. Google shows no other person with that name. But could Kasoinah somehow be connected to the French surname Gascoigne? The "-nah" syllable in Kasoinah is not too dissimilar to the "-gne" part of Gascoigne, if pronounced Gallically. If you say these names aloud, and even in different ways, they do share some characteristics. But Kasoinah is just too unlikely a surname if it belongs to only one person, which appears to be the case. It is some sort of flawed transliteration or misremembering, but I can't tell.