The board of directors of BancorpSouth Inc. has unanimously appointed James D. Rollins III as the company’s new chief executive officer, the company announced today. He will succeed Aubrey B. Patterson and become a member of BancorpSouth’s board of directors on Nov. 27. Patterson announced his intention to retire earlier this year. Rollins, 53, has served as president and COO of Houston-based Prosperity Bancshares Inc. since April 2006 and was senior vice president of Prosperity Bancshares…