I don't know what the name is, but I've seen Chinese and Japanese texts use that and the closing bracket (which looks like a stunted L) to denote dialogue, similar to the quotation marks used in English.
It may not specifically be those symbols, though - I feel like they were less rectangular and more square. Quotation marks have also become pretty common now, so it doesn't always apply...
Also, it wouldn't make sense for that to be the main usage, since these are English/American keyboards.