Sony Music Entertainment Inc. (sometimes known as Sony Music or by the initials, SME) is an American music corporation managed and operated by Sony Corporation of America (SCA), a subsidiary of Japanese conglomerate Sony Corporation. In 1929, the enterprise was first founded as American Record Corporation (ARC) and, in 1938, was renamed Columbia Recording Corporation, following ARC's acquisition by CBS. In 1966, the company was reorganized to become CBS Records. In 1987, Sony Corporation of Japan bought the company, and in 1991, renamed it SME. It is the world's second largest recorded music company, after Universal Music Group. 

In 2004, SME and Bertelsmann Music Group merged as Sony BMG Music Entertainment. When Sony acquired BMG's half of the conglomerate in 2008, Sony BMG reverted to the SME name. The buyout led to the dissolution of BMG, which then relaunched as BMG Rights Management. Out of the "Big Three" record companies, with Universal Music Group being the largest and Warner Music Group, SME is middle-sized.
What were they called after the merger
In 2004, SME and Bertelsmann Music Group merged as Sony BMG Music Entertainment