Not only is a weird request, it would make me completely second-guess your sanity.
For one, who actually asks their boyfriend if they can STALK the boyfriend's ex? Second, why spend any time stalking his ex? Why do you care? Why does it matter? If there's some sort of trust issue, then perhaps you need to leave the boyfriend alone. Stalking his ex is not the answer.
Why not just ask him about her and leave it at that.
Stalking is not an okay pasttime, despite what Twitter, FB, and all social media will have you think. It reeks of suspicious and morbid curiosity. Leave it alone. Just be happy you're with him now.
(And since that advice will go completely unheeded...just ask her what her name is. Don't tell him you WANT to stalk her. That just sounds creepy and I might have to break up with you.)