Call signs are uniq to each individual ship, world wide. As said earlier, names are often given to more than one vessel.
In Germany all call signs are starting with "D". you can read further information from the cs, eg if the ship is registered in a registry for sea going vessel.
The reason to send out the MMSI on vhf ch16 is to make sure that the DSC is matched by the voice communication.
this site is useful, same information is available to MRCC's world-wide:
This way MRCC's know who sent a DSC distress, what size of tugs might be needed, how many people are in need of help, etc. And whom to inform on land.