Complex sentence: Sinatra renamed the group "the Summit", but the media referred to them as the Rat Pack, the name of its earlier incarnation led by Humphrey Bogart and Lauren Bacall.
Split into simpler sentences: Sinatra renamed the group "the Summit". The nickname caught fire and they were referred to as the Rat Pack, the name of its earlier incarnation led by Humphrey Bogart and Lauren Bacall.