Why did the RLDS change its name to the Community of Christ? There are a lot of people under the impression that the Reorganized Church of Jesus Christ of Latter-day Saints changed it's name to the  Community of Christ in order to distance it's identity from the LDS church so they could be accepted into the World Council of Churches.

For what reason did the RLDS change it's name?
That is indeed the reason.  They sought and received guidance and instruction from the Saint Paul School of Theology and one of the first things to be changed was the name of the church (in 2001). 

Source: Mulliken, Kenneth Robert (2011). Historical Amnesia: Corporate Identity and Collective Memory in the Reorganized Church of Jesus Christ of Latter Day Saints, 1915–2001 (Ph.D. thesis). University of Missouri-Kansas City

Acceptance into the larger Christian community was eagerly sought in 2002 but rebuffed by the World Council of Churches in 2004 until finally granted in 2010 by the National Coincil of Churches.