There are multiple artists with this name:
1) Smitten was a dream pop band from San Francisco, USA, formed by Damon Fries (guitars, keyboards) and Ala Sharon (vocals). In 2004 they changed name to Boudoir.
2) Smitten is an indie rock band from Argentina. The group was founded in Buenos Aires in 1994 when two friends, Paulo Funes Lorea (Chuk) and Patricio Esteban Castelao (Patrick Steve), started playing covers with acoustic guitars. Later, some of their friends joined them, Ariel Roman, Nicolás Garoni y Pablo Molla, and formed The Nerds for some gigs in their town.