They could do that with the logos on the car, but not with the actual name of the engine supplier.
The team name and the engine supplier are fixed for the whole season unless something changes. They could still cover the cars in different logos (like McLaren did with Verizon in Austin), but the team name would remain the same.
It will be interesting to see if RBR change their constructor name to Infiniti Red Bull Racing Renault, or if they drop the Renault off the end.
Actually no, just checked, F1 constructors are always labeled chassis-engine, so it would be Red Bull - Renault or Red Bull - Infiniti. And I'm not even sure they could do that as the name in the chassis or engine constructor bit needs to be the company or individual that owns the interlectual property. I wonder if Renault would be able to use Infiniti as a name?
So it looks like the team will become Infiniti Red Bull Racing while the constructor will remain Red Bull - Renault.