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).This is what I meant about them coming in the second age. Wait, no names are recorded, then he proceeds to give them names? O_O
Edit: After doing a bit more research, found this. They were also giving these names: Morinehtar and Romestamo, darkness slayer and east helper.