MediaShout does allow the renaming of Stanzas, but only if that Stanza is not in use. For example, if Verse 1 is actually the Chorus, and a Chorus is already in the Playorder, then renaming it calls it Chorus 2. So this is what I usually recommend.
1. Open the Insert Lyric dialog.
2. Select the Lyric.
3. In the Stanza list in the center of the window, click the Edit button. (the one with the Pencil on it)
4. Change the Stanza type by clicking the Stanza dropdown. Select a type that is not being used such as Interlude for ALL stanzas.
5. Click the Edit button and proceed to the next Stanza.
6. Repeat steps 3-5, but make sure you rename in sequential order. Example, what ever is Verse 1, do that first, then Verse 2, do that second, etc.etc.