Many superheroes (and villains) in the Marvel universe are known to have more than one moniker. Ronin is actually a great example, since many superheroes, like Clint (aka Hawkeye), Maya Lopez (aka Echo), and Matt Murdock (aka Daredevil), have used the identity at various times.
So, does Kate Bishop have any other names that she goes by, other than Hawkeye? She absolutely does. In the comics, Kate is also known as Hawkette, Lady Hawkeye, Hawkingbird, and Kate-Hawk. However, her official moniker is the same as the man who inspired her to become a superhero.
At the end of the Hawkeye finale, when Kate is running possible superhero names for herself by Clint, including Ladyhawke, Hawk Eve, Hawk Shot, and Lady Arrow, he says he has an idea. Audiences don’t get to hear what exactly that idea is, but it’s likely that the Avenging archer is referring to his own alias.
Hawkeye is available to stream on Disney Plus.