The way I always understood it, Dracula revives two ways: 1) after 100 years, his body regenerate and his power builds allowing him to resurrect on his own; 2) his minions/worshipers gather his physical remains and make a human sacrifices over them; 3) Dracula's soul is summoned and enters someone with with dark powers connected to him (example: Issac in CoD) and thus that person becomes his vessel.
Regarding the Sorrow games, Soma is that literal reincarnation of Dracula. The others such as Dimitri and Dario from DoS were merely born at the exact moment in which Dracula was destroyed in 1999, thus they received some of his power. The same goes for Graham from AoS. If anything they were meant to be his servants and perhaps his vessels if he needed them to be. But, Soma was literally Dracula reincarnated. He just chose not to embrace the darkness and become what he was in his previous life.
As for why Death attacks Soma in AoS and DoS, I don't know. Assuming that it's cannon, in the novel, it's pretty clear that Death knows that Soma is his master reincarnated. If I remember correctly, Death even asks Soma to return to the castle and be his master once again.