Hello, there!
They are both correct. Their use depends on what you want to say and/or the context.
Hear of someone/sth is a transitive phrasal v. and means to get to know about someone or sth BUT watch this (your question did not involve this bit but I thought you should know): not hear of sth means to refuse to let sb do sth especially because you want to help the,.
Hear about sb/sth is an idiomatic expression and it means to learn about someone or sth (but not necessarily by hearing).
Although their meaning does present any obvious differences, their use does:
Have you heard about what happened to me when I was on vacation?
It means have you been informed about....., Have the news reached you?
Have you heard of him? Has he perhaps called or emailed you?
Here, the question asks whether you had news of a certain person or not.