The Michelotto-prepared 458 that is homologated for the GTE class is called the Ferrari 458 Italia GT2.
Determining the actual, official name of some GT racing cars can be really confusing sometimes, especially with regulation changes in some years. Back then in late 2010, when that car was revealed online, it was referred as the
458 GTC by Ferrari themselves.
See here for reference:
http://www.ferrari.com/English/Scud..._458GTC_takes_its_first_steps_at_Fiorano.aspx
In 2010, if I recall correctly, we didn't have class names of GTE Pro and GTE Am in both Intercontinental Le Mans Cup (which became World Endurance Championship) and Le Mans Series yet. For GT racing cars, we had GT1 and GT2 in both racing series. GTE Pro and GTE Am came in 2011, I believe. And as far as I know, in 2011, cars that were previously eligible for entry under GT2 category could participate under the GTE classes. More or less, GTE was like GT2 with a different name. Only that GTE Pro was for professionals and GTE Am was for amateurs. As for GT1 in either Intercontinental Le Mans Cup or Le Mans Series...well, it's gone. So no cars like the Aston Martin DBR9 in both racing series during that year.
And yes, there were other racing series out there where the car you highlighted in bold was eligible to take part, which I won't speak much of. It will get very convoluted with all the various class names. It's also eligible for entry under GT class in the 2011 American Le Mans Series season, just for example.
Well, anyway, after some teams began running that car in the various racing series, starting from 2011, many people, ranging from fans to the media, began calling it different names. Sometimes it's still called 458 GTC. Sometimes it's called 458 GT2. Sometimes it's 458 Italia GT. Sometimes the word Italia is there, sometimes it's not. So, yes, it was getting pretty confusing.
Anyway, as I stated, Ferrari originally referred to it as the 458 GTC.
But...wait! They call it
458 GT2 here:
http://corseclienti.ferrari.com/2014en/championship-type/gt-competitions/
And when Luca Cordero di Montezemolo spoke of their interest in returning to the 24 Hours of Le Mans as an LMP1 works team, he referred to the car as the
458 GTE:
http://www.gtspirit.com/2013/12/17/ferrari-boss-luca-di-montezemolo-speaks-on-le-mans-comeback/
So, err...now what.
I don't really know what to call the car.
Oh well, what am I trying to imply anyway. I am getting a bit confused myself.
I guess that Ferrari didn't seriously plan to officially name the racing versions of their 458 Italia. It's not like how Porsche named their GT3-spec car the 911 GT3 R, and the GT2-spec/GTE-spec car the 911 GT3 RSR. (I'm talking about the 997 generation particularly here)
If one very particular race car, ran by a certain team, under a certain class in a certain racing series, from a certain year, makes it to the game, I'll freely let PD does the naming job.
Say, for this one, it would be like:
#71 AF Corse Ferrari 458 Italia GTE '13
and they can name the "base model" as:
Ferrari 458 Italia GTE Base Model '13
Similar to what they did with the other race cars.
Umm...wait, what was I trying to say anyway?