spider-woman
A Marvel superhero, civilian identity Jessica Drew. While she is considered one of the various Spider-heroes in the Marvel multiverse, her origin, powers, and most of her stories are largely separate from Spider-Man.
Spider-Woman's Ultimate universe incarnation is an exception however, as she is a female clone of Peter Parker.
The Spider-Woman mantle has also been briefly held by other female Spider-heroes such as Mayday Parker/Spider-Girl and Gwen Stacy/Spider-Gwen. Most of these cases were only temporary, or only used by that character in their home universe, and neither changed costumes to go with the name.