iTunes windows alphabetize new purchased songs in purchase playlist

If you're referring to the automatic Recently Added Playlist, there is no option to show songs in alphabetical order.

However, if you create your own Smart Playlist, you can arrange it as you wish. To create the Playlist:

• • click on File / New / Smart Playlist. A panel like the one shown below will appear:

• • Click on the Artist drop-down menu and change that to Date Added. (This will cause the next box to change to is, but that's fine)
  • change the second drop-down (which now says is) to is in the last
  • change the number box (that will appear) to the number of days you would like to be included. The Playlist will now look like the one shown below:

• • click OK
  • the playlist's name will be highlighted in blue, so that you can rename it to whatever suits you (it must be unique though)

Now that the Playlist exists, you can arrange the songs into alphabetical order by:

• • clicking on View / Views As / Songs
  • then click on View / Sort By / Name

That's it.

You're welcome.