I'm afraid some answers have been wholly wrong.
The sentences are both correct, they are both in Past tense, and there is no significant difference in meaning.
Let me clear up this nonsense about Passive and Active. Note that 'Passive' does NOT mean 'I feel emotionally disconnected'. It is a strict grammatical structure, like this:
Active: My cat ATE a bird. Past simple.
Passive: A bird WAS EATEN by my cat. Past simple.
Active: It IMPRESSED me that ... Past simple.
Passive: I WAS IMPRESSED ... Past simple.
Many people are the victim of an old myth that using the Passive voice is somehow wrong or ineffective. Yes, sometimes it is, but sometimes it isn't. It is always up to the writer to decide.
My personal choice would be 'I was impressed that she remembered my name', as the other sentence strikes me as rather formal.
But I repeat, this can only be a personal choice. Both sentences are perfectly correct, and there is NO significant difference in meaning.