Should the Toyota Matrix be listed as simply "Matrix" like the badge on the car says, or "Corolla Matrix" like the owners manual and other literature states?

On Wikipedia they say "occasionally referred to as the Toyota Corolla Matrix", but as on the Toyota website it seems to be listed just as "Matrix", I guess we can list it in that way too.
It is like the Renault Scénic of 2nd generation, it is registered as a Renault Mégane Scénic like for the 1st gen, but they never call it like that anymore.

okay thanks Antoine, Honestly I had only heard of them being called "Matrix" until yesterday. I was at the Toyota Dealer getting my Corolla seviced and I noticed that my owners manual said "2009 Corolla and Corolla Matrix"