In the game, the spell is called "Righteous Might." This is the spell that Adepts have. In the files, it might be listed as "bloodlust" for the developers' convenience. And essentially, it might be the "bloodlust" from previous installments. But for Heroes 5, it's more accurate to call it "Righteous Might."
For example, in Heroes 5, we have a hero named Cristian, who is a specialist in ballistae. In Heroes 3, there was also a hero named Cristian who was a specialist in ballistae. But here, they decided to rename him Vittorio.
Perhaps the most amusing example of this is Axel, who is Klaus, who is Sarge.