Hi ge3, and welcome to the forums,
The iPhone lets you move your apps around however you like, there is no way to organize the app icons by name on the home screens,, but there is a feature that allows you to view all of your apps alphabetrically.
If you keep swiping from right to left, you will get to the App Library. if you swipe down while at the App Library you will see all of your apps listed alphabetically.
One nice thing about this is that you can also hide an app from the home screen, but it will be available in the list.
I hope that this helps with what you are trying to do.