You're almost right, but not quite; a variable variable takes the form of ${"name"}, so what you're looking for is something like global ${"arrayname_$name"};.
http://www.reddit.com/r/programming/comments/dst56/today_i_learned_about_php_variable_variables/c12np38 is fascinating reading on the topic, if you feel so inclined.
It's likely a terrible idea, though, and if you're resorting to that sort of thing, it's a good indication that your code may be poorly designed. Consider refactoring it (for example, to keep a single known array that your other arrays are kept in, and may be referenced by key.)