Do pets really know their own names?

My dogs know their names, and have an understanding of almost all the things we say to them. Food, bath, lead, walk, play, fetch, my children's names and wake them up. My dog always.. wakes my younger child in the mornings when we tell her too. She also cries when we mention our older son as she now lives in the university campus.
I bet they understand everything.. Oh she also knows her caretakers name.. When we go away on holidays we leave her with him.
They also know your moods and respond so well to you when you are happy, angry or sad.