Callsigns are great for DX, which does happen on '446 (I managed 79 miles a few summers ago, handheld-to-handheld). They're much quicker and easier than saying "I'm the OTHER dave from near Newquay" etc. There's no central register, and someone could use the same one, but the userbase is so small it's unlikely at the moment.
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There is a central register for callsigns as I have already explained if you read my previous post regarding Charlie Tango callsigns which have become the most prevalent identification method being used at present in my experience on pmr446.
It is not compulsory obviously but if you want a 'central register' then it already exists and there are hundreds of callsigns from all over the world on there and this was started in 2009 (the year I joined).
Obviously someone could 'pirate' your callsign and it would not be illegal but then again if you 'pirate' an amateur callsign what do OFCOM do? I'll give you a clue - nothing.
But you are correct it is much quicker and easier than just your name and location when DXing.