Gomez is an bluesy English indie rock band. The band consists of

Ian Ball - Guitars and vocals
Olly Peacock - Drums
Tom Gray - Keyboards, guitar, and vocals
Paul Blackburn - Bass
Ben Ottewell - Guitars and vocals

The band played their first gig in late 1996 without a formal name. They left a sign out for their friend (surname Gomez) stating "Gomez, the gig is here." People saw the sign, assumed that Gomez was the band's name, and it stuck.

Since then, they've put out 8 albums,
Bring it on (1998), Liquid Skin (1999), Abandoned Shopping Trolley Hotline (2000), In Our Gun (2002), Split the Difference (2004), Out West (2005), How We Operate (2006), and Five Men in a Hut.

Most of this information is taken from their Wikipedia page, where you can find more info on the band. Also check out their official website or visit their last.fm page to sample a few of their songs.