I got the impression that Leia and Han both either knew or had some inkling as to who she was. They both took a shine to her right away. The way they interacted with her was too familiar. They also acted pretty similarly with each other add they did to her. My guess is that this is to show either a connection or some understanding of her.
They both did take a pretty quick liking to her, but Han seemed to be genuinely surprised about her being from Jakku/wanting to go back.