No the history,surfing,computer name or IP Address can't be seen by that person because those files are saved to your computer but since the wireless network belongs to them basically you have the same ip address so the only one who can see what you are doing on the internet is your neigbors internet service provider. Don't worry internet service providers have a rule that they can't tell what your doing on the internet to protect you. Unless you're doing something illegal like downloading files from the internet illegally they can't harm you but if you do those things they can send you a warning regarding of those things you do.
