Warning! Spoilers for Hawkeye ahead.
With the Hawkeye finale released on Disney+ in the first hours of the morning and the symbolic scene of ing the baton between old-school Hawkeye Clint Barton (Jeremy Renner) and Kate Bishop (Hailee Steinfeld), questions arise on what her superhero name will be. It's not yet been set in stone to audiences when and how Steinfeld will return in future MCU projects, as there was no "Hawkeye will return" message at the show's end, with Marvel studios opting for a "Happy Holidays" message after the first end credits. Still, rumors have been circulating about the possibility of a Young Avengers project, where Kate would be central considering the comics, especially after the introduction of Kid Loki (Jack Veal) in the Loki series and Tommy (Jett Klyne) and Billy Maximoff (Julian Hilliard) in WandaVision.
Hawkeye episode 6 started precisely where episode 5 left off, with the big revelation of Eleanor Bishop (Vera Farmiga), Kate's mother, is working with Wilson Fisk (Vincent D'Onofrio). The episode saw the alliances that were seen till now shift, not only as a result of that revelation but also following Clint's conversation with Maya Lopez (Alaqua Cox). Clint and Kate could finally be seen fighting the bad guys together, as a well-functioning team, complete with a wholesome scene before the fights where they could be seen manufacturing some trick arrows together.
Befitting the last episode of Hawkeye, questions about the superhero name Kate would take soon began. As Clint and Kate talked at the very end of the episode, she jokingly proposed various alternatives, ranging from "Lady Hawk", "Hawk Shot," "Hawk Eve," and "Lady Arrow." Considering how Clint answered, saying he had the perfect name in mind right before the end credits with the show's name started, and how Kate was referred to in the comics, it would be safe to assume Kate's superhero name would be Hawkeye.
This would not only mirror the comics, but would also make sense considering how the episodes played out. The entire Hawkeye season had been about Kate eagerly wanting to learn from Clint without any doubt and Clint reluctantly accepting her help and mentoring her. Although there was hesitation from Clint's side, as shown in episode 4, in the end, the Hawkeye season finale dispelled all the doubts about Clint's approval of Kate as his successor. Not only did he seem to finally approve of her as his potential hero heir, but his focus on family seems to suggest he would like to stay out of the hero spotlight where and when possible - something that would be more possible where Kate to take on his mantle, as he could remain involved as her mentor.
Whether or not Steinfeld's Kate Bishop will be shortly seen in any MCU project, be it Young Avengers or a potential Hawkeye season 2, there is no doubt she is cemented as Clint Barton's successor. The whole season served as the origin story of her taking up the mantle of being Hawkeye from Clint. Considering how easily and organically the transition of the role went from Clint to Kate in Hawkeye, it's safe to say Kate's superhero name will be Hawkeye - if not now, then not far down the line after Phase 4 - and that she'll make Clint proud in the role that had been his for a long time.