To my knowledge, there is no way to query the dialog (conversation) that is currently running.
There is a way to provide the desired dialog ResRef in BeginConversation and ActionStartConversation (overriding the default one set in the toolset), but there is no way to read out this provided ResRef or the defaulted one (in general: the one that is to be started or effectively already running), e.g. in the OnConversation script or in any script that is called from within the running conversation.
I'd like to request a function like this: // * Returns the conversation ResRef oObject is currently in. Returns "" if oObject is currently not in a conversation.
string GetCurrentConversation (object oObject)
This way a script could distinguish which conversation it is currently in and make choices depending on it.