Does a boat have to have a name, and if it does, can it be any name?
British Waterways holds a register of unique numbers which it uses to identify individual craft using its waters. Although a name is required to be submitted with boat registrations it is not used to identify individual boats, so does not have to be unique. There are however restrictions on, for example, using an offensive name, and if such a submission were made would be reviewed on an individual basis before being accepted for use.
The Environment Agency, who are responsible for River Thames registrations, however, use the boat name as part of the identifying process, and as such each boat registration has to include a unique name. So, for example, should you wish to call your boat "Water Bunting", and there were already three other boats registered with the same name, then as per the information given on the registration form, your boat would have to be called "Water Bunting IV".
So what if you wanted to visit the Thames on your narrowboat "Water Bunting"? As you enter environment agency waters you will be issued with a temporary visitors registration name in the form of: Visitor R1234, and issued with stickers to display whilst using their waters, in much the same way that registration numbers are stuck on motorized craft using Lake Windermere.
When buying a used boat you are free to change the name as you wish, providing you follow the above criteria. However, I am a believer in leaving well alone. Although I don't particularly like the name "Kelly Louise", and it has no relevance to me, I would never change it, apart from the £500 or so cost of re-sign writing the boat.