Spider-Man is a name used by several different characters in DC Universe.
The superhero Jonathan Law briefly used the Spider-Man alias and later adopted the codename Tarantula. Spuda the Spider-Man was a circus performer in Colonel Lane's Mammoth Circus. There is a super-villain named Spider Man on Earth-S who battled the Captain Marvel. In the Quality Universe, an unnamed man has also transformed into Spider Man and fought Spider Widow.
Marvel Comics publishes their own Spider-Man in an ongoing series. DC Comics has published several homages to this character. The original was Cobweb Kid, a character from the Inferior Five comics, and later a member of the Maximums named Bug and a member of the Retaliators with the same name. In the Amalgam Universe, Spider-Man is mixed with Superboy and Mon-El to become Peter Ross and Mig-El Gand respectively.