Mentally freak out, but appear calm on the outside, so he wouldn't think I'm some misceláneo freaky fangirl. (Which I am, but that's beside the point.) I'd ask him to keep quite so that no one would hear him, and then ask him how and why he got to my room, what he was trying to do (because he can control where he wants to teleport to, hense Chaos *Control*, and I'd doubt he'd try to go to my room...), then after he seems comfortable I'd ask if I could come with him to help with whatever he's trying to do... Yeah.
I would mentally scream curse words and preguntas at myself, but try to hold in my excitement on the outside. Also I would ask him how did he even get here since the hedgie can control Chaos CONTROL (it's in the name genius 😝) and say what can I do to help him get to his REAL destination. If Shadow teleported to my room, (this is reason 2) I would kinda get scared and hide behind my wittle bunny -w-. Then, once I calm down, I would say hello politely (NOT get like an insane fan freak who has life sized posters hanging in her freakin' bedroom😓) And obviously do what I can in my power to help him. XD
I would say "Shadow The Hedgehog?!" Then i would rub my eyes to make sure I'm not dreaming then I would feel like passing out but I have to keep it together. Then I would say "Shadow, it's an honor to meet you."