Complex sentence: He took the name of Victor Borge, and, in 1941, he started on Rudy Vallee's radio show, but was hired soon after by Bing Crosby for his "Kraft Music Hall" program.
Split into simpler sentences: He took the name of Victor Borge, and in 1941, he started on Rudy Vallee's radio show. He was hired soon after by Bing Crosby for his "Kraft Music Hall" program.