There are several artists using this name:

(1) Costello is an Irish hip hop emcee and member of Street Literature. His music has been released by Workin Class Records and his debut album Illosophical has received national praise for its sophistication in rhyming and superb production contributed by G.I.

http://workinclassrecords.com/
https://www.facebook.com/pages/Costello/273706839350000

(2) Costello is a 4-piece melodic punk/power pop band hailing from Los Angeles, California. Founded in 2003, Costello has become a staple of the west coast punk scene with their hook-laden brand of melodic punk and power pop.

In the summer of 2004, Costello was signed to the nationally distributed independent record label High School Records. The following year, they released their debut full-length LP titled Scatterbrain.
In 2007, Costello released a second full-lenth LP entitled In Vino Veritas. The album was generally well received by critics and listeners, and helped further establish the band''s signature sound.

(3) Costello is a 23 year old French DJ/Producer hailing from Bordeaux. Inspired by techno and house culture, he creates sets which showcase his own creations, productions and remixes. Recently signed to Boxon Records (FR), Big Fish (CA) and Dim Mak (US).