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Interesting! She seems to have been the only bearer of the name in that form. It doesn't occur as a surname or given name in the UK with that spelling; however, there is a Cornish surname Trestrail (pronounced treh-strayl) which apparently means 'homestead of mat or carpet maker'. According to Trestrail family researchers, there was a family of that name in Illogan - where the Titanic survivor's mother was from - in the 1500s, spelling it 'Trestreale'. So given a lack of any data on 'Treasteall', I'm guessing that it was a family name that originated from some spelling of Trestrail, and either the passenger list transcriber made a spelling error with the little girl's name, or her mother used some kind of ancestral variant spelling - or simply couldn't spell all that well.
Anyway, that's probably more than you wanted to know! - but given all that, I'd probably pronounce it treh-stayl.

This message was edited 4/19/2014, 6:02 PM