There is nothing to stop them calling themselves 'slimboy fat' 'fatslim boy' or even 'lim boysfat'.
On a side note:
Band names are in fact territorial
On the other side of the coin,it may even surprise you to find that if your band was called 'led zepellin' before that particular band became territorialy famous,i.e. 'world famous' that 'led zep' would have to change their name when playing in your home town.
Quote: "www.music-law.com
If you started using your name first, you can prevent others from using it. However, the law allows you exclusive use of the name only in the area where you have used it. For example, if you started playing the Chicagoland area in 1989 and never played or distributed music outside the Chicagoland area, you could not prevent a band from using the name in Florida."
However as they are using a derivative of said name even this does not apply.
Since this is not even a band you can call it what you like
I like the three year olds choice all the same.