This is something that has always puzzled me.
As far as I'm aware, the US version of WoW has always had the option to generate a random name when creating a character. The EU version however, has never (iirc) had this option after so many years.
I see no reason why it would be in one version of the client and not in another. They are quite basically the exact same thing except having access to different servers. Why would such a simple little feature be left out?