This is cool (and, really, required at this point to be competitive) but why can't they use a self-explanatory name?

Amazon calls their SSD-backed volumes "General Purpose (SSD)" and "Provisioned IOPS (SSD)" which explain themselves. Azure Premium Storage could mean anything (and when it's the norm in a couple of years, what will they call it then?)

Super Premium :-) I think the way we think about it here is: Azure "Premium" Storage as opposed to the regular Storage offering we have. Having said that, our naming could have indeed been better.

Disclaimer: msft engineer with Azure Storage