Do pets really know their own names?

I feel that our pets know their own names without a doubt. The first example would be that they respond to when we call them which means they remembered that the sound we call corresponds to themselves. I love how fast my cat realized this which just shows the intelligence level that our loved pets have. I feel that if someone doesn't agree with what I have posted it means their pet may be called by different names during the day which makes it hard for them to understand that they only have one main name.