Eilleen Regina Edwards was indeed, by most accounts, Shania Twain's birth name. Wikipedia spells her first name in the normal way ("Eileen") in its introduction, but opens its Early Life section with the statement "Twain was born Eilleen Regina Edwards in Windsor, Ontario, on August 28, 1965".
Her parents divorced when she was two, and her mother married Jerry Twain, a First Nation Canadian with Ojibwa ethnicity. Jerry adopted Eilleen and her two sisters, and their surname was legally changed to Twain.
Eilleen started using the name Shania around 1993, when she signed her first recording contract. The name has been said to mean "on my way" in the Ojibwa language, but there is a considerable amount of scepticism about this. It would appear that at best, it's a very approximate rendition of something that might mean something about somebody being on the way.
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