I'm confused, so has the Lotus team from last season got the proper Lotus racing name but not official backing from the manufacturer and what was previously the Renault team got it the other way round ?
It is very confusing.
There are TWO Lotus companies, both originally owned by Colin Chapman. The first, Team Lotus, was the racing team producing mainly F1 (but also F3) cars. The second, Group Lotus, is the road car manufacturer. The two companies were (and are) totally separate.
Team Lotus went bust in 1994, and was bought by David Hunt who lacked the money to keep it going, but kept the company ticking over.
Group Lotus (via a few other companies) was bought by Proton in the late 1990s.
Tony Fernandes brought back the Lotus name last year, by a licensing deal with Group Lotus for use of the name "Lotus", hence "Lotus Racing", not "Team Lotus", which wasn't within Group Lotus's remit to give. Fernandes did a deal with David Hunt to buy Team Lotus, hence Lotus Racing became Team Lotus, and announced way back in September that they would be using the old JPS black and gold colour scheme in 2011.
Group Lotus have now bought Renault F1, and are now claiming that "Lotus is back in F1", which is utter nonsense because Group Lotus have never been in F1. And they've decided to go for a black and gold colour scheme. Indeed, Group Lotus aren't allowed to use "Lotus" in F1, only Team can do that. Group are also claiming all of Team's historical achievements.
The upshot is that Team Lotus (which have done a deal with Renault for engines) is now "Lotus Renault".
Group Lotus now sponsor the Renault F1 team, and so are called, yes, you guessed it, "Lotus Renault".
There's a court case going through the High Court right now about just who can be called "Lotus" in F1, but my money's firmly on Tony Fernandes winning.