Complex sentence: After a tour with Joe Cocker, some more of the personnel from Delaney and Bonnie joined up with Clapton; he attempted to avoid the limelight in a group dubbed Derek and the Dominos, and booked a British tour of small clubs.
Split into simpler sentences: After a tour with Joe Cocker, some more of the personnel from Delaney and Bonnie joined up with Clapton. He attempted to avoid the limelight under cover of the anonymous "Derek and the Dominos", booking a British tour of small clubs.