Hermione is a Greek name, meaning eloquence.
JK Rowling chose the name Hermione from a Shakespeare play, "A Winter's Tale," although she says that the characters are not at all similar. She thought it made sense for a couple of professional dentists to name their only daughter something like that to show how clever they were. But she chose a very unusual name because she worried that, if there were a real child somewhere who was bright and had larger-than-usual front teeth that had the same name, she might get teased.
Hermione
"The name of Hermione gives you a responsible, reserved, and dignified nature, able to find a certain amount of success in anything you undertake. You have an appreciation for the finer and deeper aspects of life. Your scholarly, studious interests incline you to art, literature, philosophy, music, and drama. You wonder about the deeper aspects of life contained in religious theories and occult beliefs. Others may consider you to be aloof and unemotional since you often find it difficult to express spontaneously. They could interpret your quietness as disinterest and aloofness, for they do not realize the depth of your feelings and thoughts. You require time alone, especially in the outdoors, to cope with the pressures of life. This name causes tension to affect your heart and respiratory organs, resulting in colds or bronchial conditions."
Granger
"Your last name of Granger has given you a rather quiet, reserved, serious, studious nature. You have sensitivity and appreciation for the finer and deeper things of life, the beauties of nature, music, art, and literature. The people who mean the most to you are those who can offer you intellectual companionship. It is only when you are among those who understand your deeper nature that you can really be yourself. The experience of having your remarks taken lightly or belittled, particularly during the early years of your life, has caused you to keep your thoughts and feelings to yourself. You do not express yourself spontaneously when conversing with others; hence other people may often regard you as being aloof, and even unfriendly. Your difficulty in putting your deeper thoughts and feelings into words can lead to problems in more intimate associations. This name has caused you to live much within yourself. You are rather easily hurt or offended. At such times you can withdraw into a mood, and may not even speak to others. Aside from these points, this name contains many fine qualities. You are a thoughtful, analytical person, and you know your own mind, even though you may not speak it. You are very conscientious and competent in all that you do. You take seriously any responsibilities that you have--in the home, in the community, or at the job. Worry and mental depression could be problems in your life. Physically, any weaknesses in your health would centre in the heart, lungs, or bronchial organs."