The camps for the most part had both official and unofficial names- one that the military government came up with and the other that the workers and internees in the actual camp used. I haven't found anything for a "Camp Churchill", maybe it was called that by the internees because Churchill was one of the leaders who pushed for the DP camps.
The area occupied by the western allies was broken up into British, French and American zones, the Russians had the eastern half of the country. There was a Churchill Barracks in Celle, basically a large military barrack area the British took over in 1945. Celle itself was in the British Zone, but after the war there was quite a bit of interaction between US and British forces and US forces handled a large portion of the DP issue for the allies, that could explain the memories of US troops.
Here is a general map of the zones
http://www.dpcamps.org/dpcampmap.jpgA generally good overview of the end of the war and conditions of the occupation
http://www.history.army.mil/books/wwii/Occ-GY/