Unless you know the password for the ID you won't be able to get any details about it. You can't get a list of IDs using your name for privacy reasons, as many people might have the same name as you.
No one can set up an iCloud account and "monitor" your phone but you. Your phone would need to be signed into the iCloud account in Settings>iCloud, which someone couldn't do without having your phone.
If you want to enquire further about what you can and can't find out about this, you can contact iTunes store support: https://ssl.apple.com/emea/support/itunes/contact.html.