No, The Damned is not a goth band, because they play Punk Rock, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

However, they do have a significant goth influence and even have some goth songs in their repertoire, like "Street Of Dreams" and "The Shadow Of Love".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy The Damned are 45 Grave and Specimen.