Why was Túrin called "Turambar" (Master of Fate/Doom)? Is it something to do with the Second Prophecy of Mandos?
It's "Master of Doom", and he made up that name himself:
And with the beginning of spring Túrin cast off his darkness, and grew hale again; and he arose, and he thought that he would remain in Brethil hidden, and put his shadow behind him, forsaking the past. He took therefore a new name, Turambar, which in the High-elven speech signified Master of Doom; and he besought the woodmen to forget that he was a stranger among them or ever bore any other name.
-- The Silmarillion, "Of Túrin Turambar"
So in giving himself that name, Túrin is basically saying that he plans to escape the curse by abandoning his past and going native among the woodmen.
It doesn't work.