Do I need to change my CV when a former school changes affiliations?
I think the best approach is to keep the original CV entry, as this represents the actual qualification that you received. However, you might choose to add a note explaining the history, if you think this is likely to be helpful to prospective readers. 

I agree that in the case described by @brechmos, where a university has changed its name, providing this information is likely to be useful. It's less clear to me that this is true in the OP's case: it seems (essentially) that the qualification he has used to be accredited by University X, and is now accredited by University Y. It's not clear to me why this would be useful information to someone reading the CV. I guess it might be relevant if the training centre has a high enough profile that people now naturally associate it with University Y, and would think that something listed with University X must be a different centre. Otherwise, I suspect noting the change is more likely to confuse people than help them...