Well, tbh whenever SHs do something significant, it's Luffy who gets the most (if not all) the glory... Like with Dofla, every newspaper mentioned how Luffy was such a badass, but what Zoro or Ussop or any other SH did got no attention from anyone. Right now he's just a member of Luffy's crew, he doesn't have any personal identity, so I don't think they care wether he's a 'Pirate Hunter' or something else.
Maybe it'll change after Wano, when Zoro, Sanji and others take on Ultralords of New World and make names for themselves like Shanks's crew.