The international standards for distress and urgency VHF calls are specified by the ITU for all signatory countries (pretty much all countries are signatories), and they have a provision for using the ship's call-sign .
I found this on the Coast Guard site. It specifies Name and
Registration number or Call sign(my highlight). Link to the page below.
Procedure for VHF Channel 16 MAYDAY:
If you have an MF/HF radiotelephone tuned to 2182 kHz, send the radiotelephone alarm signal if one is available. If you have a VHF marine radio, tune it to channel 16. Unless you know you are outside VHF range of shore and ships, call on channel 16 first.
Distress signal "MAYDAY", spoken three times.
The words "THIS IS", spoken once.
Name of vessel in distress (spoken three times) and call sign or boat registration number, spoken once.
Repeat "MAYDAY" and name of vessel, spoken once.
Give position of vessel by latitude or longitude or by bearing (true or magnetic, state which) and distance to a well-know landmark such as a navigational aid or small island, or in any terms which will assist a responding station in locating the vessel in distress. Include any information on vessel movement such as course, speed and destination.
Nature of distress (sinking, fire etc.).
Kind of assistance desired.
Number of persons onboard.
Any other information which might facilitate rescue, such as length or tonnage of vessel, number of persons needing medical attention, color hull, cabin, masks, etc.
The word "OVER"