I'm surprised this hasn't been asked before but I could find any question on here for it.
Who picks the tail number for a new aircraft?
Is it automatically assigned by the authorities you are registering with or can the new owner pick any number as long as it's not already I use?
If it's auto generated by the authorities, can you purchase the equivalent of a custom car registration plate if you want a specific number?
I've tagged CAA but would be interested to know if the FAA is the same.