Honey4ever wrote: … I was expecting there would be a way to organize them alphabetically
Yeah, I get that. Unfortunately, there is no automatic ordering of albums in iOS. Those of us with Mac do our arranging in Photos there, and the Mac version does have alphabetical sorting. I'm sorry--that's no help for you.
You can search for an album by name. Even so, the best way to keep up with hundreds of albums is to put them into folders so they are more manageable.
In Photos, albums can be in folders, and folders can be inside bigger folders. This is my Main window in Photos:

I have pictures arranged by date, for instance. The first folder has 6 other folders in it, as well as 11 albums that are not yet in folders. It makes finding albums way easier. (There are also folders with albums that are not by date-- pictures can be in several albums.) Doing this isn't hard on a phone if it's done as pictures come in, but the idea of putting hundreds of pre-existing albums into folders sounds untenable!
iOS still has no way to put a pre-existing album into a folder. Your only option is to create an empty album in the folder, and then select all the pictures in a pre-existing album and "add to album."
Well, the other option is to borrow a Mac where you can drag albums into folders and alphabetize them, then sync to your phone. Oh, well…
I'd suggest you leave a suggestion for Apple here:
Feedback - Photos - Apple