One way is to interrogate the latest records written to the RSPC_CHAIN_LOG (or similar, sorry don't have a session open at the moment), and find the most recent LOGID for the chain name. This is how SAP do it.
Another way is to create your own function module that runs in background. What it does is launch the chain using the standard CALL FUNCTION MODULE and retrieves the logid. Then write the logid and process chain name into your own table.
Another way that might work, not tried it, is to use CALL FUNCTION MODULE ... STARTING NEW TASK CALLING meth (PERFORMING form) . This allows you to WAIT until the FM is finished, and runs the method meth, or the FORM form, which RECEIVES the e_logid.