On Rhapsody, if you press on a playlist name for a few seconds you open up a menu that offers options including rename playlist. Very simple. (I'm using both services now, and Rhapsidy surprisingly has many features lacking in Spotify.)
Seriously Spotify. I figured that maybe like FaceBook it would be a pain but I could log in through Safari and rename my playlist there. But no I have to dig out my laptop?
How has this still not been added to the apps? It's starting to feel like Spotify is always a few years behind with adding features. Features that should've been in there from the start.
Updated:
Hello everyone,

as mentioned, this should now be implemented.
At the top of the Playlist just tap on "Edit" and then on "Rename" to change a Playlist name.
Thank you for adding kudos to this idea here! 😉