According to Wikipedia, these were names that were suggested (although it was Transatlantica, not Transatlantia). "Considered" may be putting it a little strongly.
In truth, according to Wikipedia, the name Canada was "unanimously accepted ... [with] little discussion" in 1867, when delegates from the three Provinces (Canada, Nova Scotia and New Brunswick) met in London to agree the terms for their merging into one federation.
No one really knows where the name Canada came from. The most widely-accepted version is that it came from the local Iroquois name for a village or settlement (kanata). It has also been suggested that the same locals had learnt the phrase ca nada ('nothing here') from early Spanish or Portuguese explorers, and it was with these words that they greeted the later (French) visitors. There are other, even less convincing, explanations!
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