That's not stalking. Stalking is when you find personal information about them using different sources rather than asking the person. And I mean like, watching them and following them and crap. THAT'S stalking.
When you love someone of course you want to know everything about them.
It's not necessarily obsession, but some girls do take it too far.
I would say that someone like that is just greedy, but is still somewhat lustful. Lust doesn't only mean want to ... y'know with someone. It's also when you have to have physical contact with that person 24/7, basically.
Hoped that cleared some things up.
(: