Can an illiterate fortune teller give a name?

Not necessarily. Most fortune tellers don't know their names, but they know how to tell fortune. Names are based on the ups and downs of the eight characters and five elements, to decide what words are appropriate. For example, if the eight characters are short of wood or the wood is too weak, it is necessary to make up the five elements of wood or words with the meaning of wood. This requires mastering the attributes of the five elements, the meaning of the words and the number of strokes of a large number of Chinese characters. If you just tell fortune, you don't need to learn these things. So you can tell a fortune. You don't have to have a name.