Well, if you ask me, having a yandere girlfriend when yourself is supposedly doing a double identity as the local superhero is a big plus. Now you don't have to worry about her safety, just your own, doubled.
Edit: Just realized the "Desu" in her name is supposed to be "Death" (pronounced Desu in Japanese), so her true name should be "Death Helene", a foreshadow and fitting thanks to the fact that she is the daughter of Deathparta's leader, who's seemingly named "Death Zeus". So yeah, her family name is "Death".