The Music app in iOS 8 doesn't have the one-step rename option for playlists that's offered in your desktop version of iTunes, but you don't need to rebuild a playlist from scratch to change its name. Create a new playlist, import the tracks from the original list and then delete the original to effectively rename a list without using iTunes.
To rename a playlist in iTunes on a computer, select it in the Playlists view, click its name and type a new name. The next time you sync your iPhone, the phone adopts the new name for the list.
Step 1: Create a New Playlist
Open the Playlists tab in the Music app on your iPhone and tap New Playlist. Give the new playlist the new name you want to use for your existing playlist and tap Save.
After creating the playlist, the app asks you to pick songs to add to the new list.
Step 2: Select the Old Playlist
Select your original playlist, rather than searching out each individual song you want to add.
Step 3: Add All Songs
Tap Add All Songs to add the entire list of songs from the original playlist to the new playlist. Tap Done to finish.
To merge multiple playlists, tap the Playlists back arrow instead of Done, select another playlist and choose Add All Songs again.
Step 4: Delete the Old Playlist
Return to the Playlists tab after you finish creating the new playlist. You'll see both the old and new playlists, each with the same number of songs. Swipe from right to left along the old playlist and tap Delete to remove it.
When you next sync your iPhone with iTunes, the playlist name on your computer is updated; there's no need to rename it in both places.