You can't change the names of songs directly on your iPhone. To change the names of songs on your iPhone, you have to first change the name of the song in the iTunes music library and then sync your iPhone with iTunes. Upon completion of the sync after the name change, the new song name will be reflected on your iPhone. You can change the names of songs in iTunes by accessing the metadata associated with those songs.
Connect your iPhone to your computer using the cable that came with the device, and then launch iTunes.
Click the "Library" tab and then click "Music" to see a list of all of the music in your iTunes library.
Right-click the name of the song you want to edit and then click "Get Info." An iTunes dialog box opens.
Select the "Info" tab.
Highlight the song name that's currently in the Name field and then type the name you want to assign to that particular song.
Click "OK" to save your changes. The dialog box closes and the name change is applied.
Click "iPhone" in the upper right corner of the iTunes program window to access the information screen associated with your iPhone.
Click "Sync" to sync your iPhone with iTunes. When the sync is complete, the updated song name will be applied to the song on your iPhone.
Information in this article applies to iTunes 11.2.2. Procedures may vary with other versions or products.