I think that her true identity is the "Goddess of Origin, Arovinasu", from the game. If you look back on the first chapter, It was the Goddess of Origin that appeared on the MC's computer screen and asked "I shall offer you a new role, do you accept?". If that's the case, It was actually "Diina" the one that summoned the MC's soul to the game world.
What lead me to think this, aside from the fact that she said that her "specialty" is teleportation and that she clearly seems to be hiding something, is that her appearance is too similar to the Goddess, specially her hair.
Also, she mentioned that when teleporting living beings, If something goes wrong, that someone might lose their "conciousness". And on the game world Lufasu got "sealed" on the hyperspace, which I think stands for being "teleported" to the hyperspace. And If the "real" Lufasu lost her conciousness, I think the only way to "bring her back" would be summoning the MC's soul to game world and placing It inside Lufasu's body. And If she really is the Goddess, I think she did that to "save the world" since Lufasu was the only one left with enough power to defeat the demons.
Anyways, It all fits the isekai genre cliché. I mean, when It's not a king of a random country that summons the person, It usually is a God who does, and It's almost always to save the world.
As for the reason of why she is hiding her identity, If all that I said is right, It could be so that she can observe the MC's actions from up close, without having to worry that the MC would hide his true nature. Because If the MC was a bad person and he knew that the Goddess of that world was watching his every step, he would probably hide his "true self".