Complex sentence: After signing with Atlantic Records it was discovered by their lawyers that the name "Mighty Joe Young" was already taken by a blues artist, so they changed their name to Shirley Temple Pilots due to their fondness of the initials "STP".
Split into simpler sentences: After signing with Atlantic Records it was discovered by their lawyers that the name "Mighty Joe Young" was already taken by a blues artist. They then changed their name to Stone Temple Pilots due to their fondness of the initials "STP".