There are few posts to find out the exact Connection name used to connect a BEx Query. There is a general way to identify it. It is through Promotion Management tool.
Login to CMC -> Promotion Management -> Create a Test Job to promote the required Webi Report for which we need to identify the Connection name.
You can find the Connection Name of the Report in the “Manage Dependencies” screen under Dependents column including the related BEx Query name.
However, this is not a standard way, just a general working way to identify it. You can delete the Test job later.