Complex sentence: Prior to the release of the "Dizzy Up the Girl" album three years later, "Name" was the band's most successful single, currently it is their 3rd most successful single after "Iris" and "Slide".
Split into simpler sentences: Prior to the release of the "Dizzy Up the Girl" album three years later, "Name" was the band's most successful single. It is currently their 3rd most successful single, after "Iris" and "Slide".