Well-known Boston advertising executive Mike Sheehan will become chief executive officer of The Boston Globe, and the newspaper company’s new owner, John Henry, will assume the role of publisher, in a pair of moves intended to remake the leadership on the business side of New England’s largest newspaper. Henry, who bought the Globe and its websites from the New York Times Co. in October, becomes the ninth publisher in the paper’s 141-year history. Sheehan will oversee all day-to-day business operations at the Globe while Henry concentrates on strategy.