I have old email address email@example.com as an apple id. How to change email address to firstname.lastname@example.org correctly? I have only 1 iOS device. Should i log out from all services and change it through appleid page or i can change it directly from iOS devise without logging out from services (iMessage, iTunes etc.)? Thanks.
I would suggest that you first sign out of any service or device that uses your Apple ID, except for your primary iOS device, if you want to use it to change your email. From there, you can change your Apple ID email address from the iCloud preferences.
Check out this article for information on how to change your Apple ID: Change your Apple ID