Hello again Tellum,
In addition to the good advice from Martin about registering your radio details, it is also very good practice to register your boat name and details/shore contact details with the Coastguard CG66
scheme. This is especially important if you have not registered a PLB with the coastguard, which asks for similar information.
If you want to check what details are held, which relate to your MMSI number or EPIRB/PLB Hex code you can check this site.
though it is notoriously out of date.
In practice for small vessels which do not have a fixed radio, your handheld callsign is usually your vessel name. I am guided on this by my friend Ian who is a senior comms officer in the RFA (formerly also the RN). On our kayaking trips we only have handheld VHFs and communicate with each other, other vessels, the coastguard and the Queen's Harbourmaster Clyde using our vessel names with no problems.