Some people say it is a False Super Saiyan God, other people say it is a Super Saiyan God 2, while another group of people say it is something different. Is there any official info on what it is exactly?
Well, it finally has an official name for the transformation. It is called 超サイヤ人怒り (Sūpā Saiya-jin Ikari) which means Super Saiyan Rage or Super Saiyan Anger. The form makes its first appearance in Dragon Ball Z: Dokkan Battle and properly named in Super Dragon Ball Heroes.
Dragon Ball Z: Dokkan Battle
Super Dragon Ball Heroes
No as of today 11/4/2016 there is no name or real explanation as to what it is or how it works. I suspect it will be revealed towards the end of the current arc.
As Kaz Rodgers correctly points outs, there are no in-universe explanation yet. However, we can try and make some assumptions.
To understand Trunks' transformation, we have to go back and revisit the time when Vegeta became Super Saiyan Blue (SSB). At first, it is explained that the only way a Saiyan can get God Ki is by performing the ritual with 5 Super Saiyans they did at the beginning of the new series. So how did Vegeta do it? His first transformation into SSB happens after he has trained with Whis and Beerus for 6 months. Therefore, it is possible that some of Whis and Beerus' God ki has rub off on Vegeta after spending so much time with them.
Now back to Trunks. With the same reasoning, we can assume that some of Vegeta's and Son Goku's God ki diffused into Trunks. However, unlike Whis and Beerus, they are not Gods and therefore Trunks was only able to get some of God ki but clearly not enough to power up to SSB directly.