I think, but don't quote me, they did take the name from the Casuals, because they were always called Casuals. I could be wrong, but whatever, a lot of history between countries there.
Corinthians got their names from our very own Corinthians (now Corinthian Casuals), good history in their closeness. I went to a Corinthian Casuals game a few seasons back and there were at least 100 Brazilians there supporting them on a cold November afternoon.
A little history link