Rename a music playlist from "Purchased" to actual album name on iPhone 6, iOS 9? I have a free music album from the iTunes store that shows in my iPhone playlist as "Purchased." I want to rename it to the album name.

Can I do that directly on the phone, or do I need iTunes? How do I do it?

If it makes a difference, then the album is U2 Songs of Innocence. You know, the album that everyone was upset about it because it suddenly appeared in your playlist, whether you wanted it or not.
You cannot rename 'Purchased' - that is where all your 'officially purchased from Apple' [whether you had to pay for it or not] music sits. 

You are free to make a new playlist &amp; copy any tracks you wish to it, exactly as you would for any playlist, on phone, pad or Mac.