Hi teachers, yes it's me again

Could you please check the following conversation between 'A' and 'B' and tell me if there's any mistakes in that?
Here's the conversation:
A: You have a very nice pet, you know. (or 'you know that?'?)B: Yes, I have.A: What's the name of your pet? Is it a he or a she? (or should 'A' say 'Is it a male or a female?'?)B: Its name is Tiger. And it's a male. (Does saying 'We call it Tiger.' sound more natural?)Thank you.