Request types appear in the same order as you ordered them when you created your request types. That is why you need to go to Project Settings-> Request Types and reorder the request types as you would like to see them in the picker.
You can read more about request types and how to manange them here:
Connect with like-minded Atlassian users at free events near you!Find a group
Connect with like-minded Atlassian users at free events near you!
Unfortunately there are no AUG chapters near you at the moment.Start an AUG
We're bringing product updates and pro tips on teamwork to ten cities around the world.Save your spot