If you don't know the person, it is probably better to include the name. If it is a formal or business message, it would be wise drop the "Hi" and simply to use the person's title, whether it's Mr. or Ms. or Dr. (or for holders of political office, Mayor or Senator or what have you), followed by their name. I am inclined to think you don't need the "Dear", either.
I'm writing to inquire about the possibility of an internship in your department. [Etc.]
This would be sufficient and would not cause offense through unwarranted familiarity and it would not come off as too casual.
If it were an email to someone you didn't know but the setting was casual (for example, you got their email address from a message board about a shared interest), you might use the "Hi" as in:
You don't know me, but we both frequent the Sprocket Collectors forum. I was interested in one of your posts and wanted to follow up on it.