Is Apple warranty transferable, say I have second hand retina I need to send in ....

I have a retina MBPr I got off someone not so long ago and it's under warranty. I have the receipt printed off the Apple site w invoice number etc. and it's in the previous owners name. Does Apple care whose name is on the receipt/record etc? Do these details need to be updated somehow ?

I am in Australia and plan to just bring it into an Apple store.

Thanks..