How interesting. When I was a child living in a suburb of Buffalo, New
York, there was a teenage girl who went to my church who was called "Chana" or "Channa"
Smith. I don't remember how they spelled it, but it was pronounced to rhyme with
Hannah.
In her case this was a pet form of
Christiana. The family explained that her older sisters couldn't pronounce
Christiana when she was a baby and it came out as "Channa".
She was the daughter of
Henry P.
Smith III, who was later a US Congressman. I can't find a reference to Channa herself on the Internet right now, but she was named after her father's mother,
Christiana Long
Smith, and you can find references to her here, explaining how
Christiana Street in North Tonawanda was named after her:
http://www.nthistorymuseum.org/Collections/citystreets.html
So yes, I do know of one case where a name similar to Chaney was used as a pet form of
Christiana.