Air Carrier Dispatcher reported a communication breakdown between Dispatch Operations and flight crew regarding a Hazmat issue during pre-flight. Hazmat issue was resolved but highlighted discrepancies with Dispatch communications procedures.

Narrative

Aircraft X delayed over an hour due to a Dangerous Goods (DG) issue in cargo position XX. While flight was delayed; both ZZZ ramp agent and service recovery asked if I had heard from the crew. I had not; yet crew was telling ZZZ ramp agents they were on phone with Dispatch. ACARS message sent for clarification; where they again stated they were on phone with Dispatch. Crew then said they called the number on the DG manifest which went to the Dispatch manager's desk in Domestic and no one there notified anyone in International; either myself or service recovery. I was never directly involved in the issue at all; other than to receive an ACARS from the crew later saying everything had been taken care of.There are three issues which lead to this. First; the crew; rather than contact their Dispatcher directly or send an ACARS; they instead chose to use a number that shows up randomly on the DG manifest. Second; the phone number on the DG manifest needs to be tailored to go to the most appropriate person if there's a question; not just default to Domestic Dispatcher. Finally; if Domestic Dispatcher is getting calls from International flights; then they need to be told to make sure to pass those to the appropriate person in International Dispatch; whether that may be the dispatcher or service recovery specialist.Fix the automatic number on the DG manifest to go to some number other than Domestic Dispatch. D.G. issues are usually more of service recovery issue than flight dispatch; so I would recommend having it default to whoever the box person is for the given flight. Continue pounding it into the crewmembers' heads that Dispatchers share joint Operational Control with the Captain and need to be involved when there are issues with a flight.