The names Alatar and Pallanto were their names in Valinor. While i'm assuming when Tolkien indicates that they don't have names, he means that they don't have names given to them by the people of the particular area (example being Gandalf called Incanus).
Edit: After doing a bit more research, found this. They were also giving these names: Morinehtar and Romestamo, darkness slayer and east helper.