I dont think the story's necessarily revolving around the Sherlock stories. Its more so he just likes using popular fictional characters popularized in our world into the transmigrated one since no one knows of these character names and he'll be all different and not like the other girls type MC lol seeing as he's used both James Moriarty (from the Sherlock franchise) and Van Helsing (from the various Dracula iterations) as aliases for differing coups and chaos-stirring shit he was up to, with the former aka Moriarty name being more popular since its where he was most noticeable by the public and authorities ^^ hope this helps hehe

Okay, now I know why he's called James Moriarty!! Please forgive me if I'm wrong but I was a bit confused why he's called James Moriarty in his other identity.. I thought this was somehow related to the world of Sherlock Holmes so everything was confusing for a while even if I vaguely understood the plot but then I realized, since he's a transmigrator, he probably just used that name as an alias and ran with it bcs of what he read from his past life (?) But I do think that the story is inspired by Sherlock Holmes, atleast by a tiny bit