Let's go over how you can attempt to reserve your name.
Let me start off by saying, this isn't exactly ideal. Thanks Amazon.
Since names are globally unique if you live in the Americas, or Asia you are going to have to get up at randomly weird time that correlates with 8am Central European Summer Time or CEST and log into the EU servers. You can go to a place like worldtimeserver.com and find out what this is in your own time zone. I'll post a link in the comments below.
You don't actually have to play the game. All you need to do is create a character and reserve your name.
Also don't wait around actually personalizing your character. Just accept it as is and get that name. Once you secure the bag if you get put in the queue you can back out and go to bed. You name is now locked to your account and then at a time that is convenient for you can go back and delete that character and remake them on whichever server you wish. The name will be bound to your account for a period of time. We aren't clear on how long so people are assuming it's at least a minute.
Players on EU, hopefully this doesn't create too big of an inconvenience for you. Please register all complaints with Amazon Customer Service.
Thanks and I'll see you in Aeternum.