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What do you do? It's certainly not stored in the undo history.

Is there absolutely no way to retrieve the name of the now deleted input field's text?

Not the end of the world but certainly MOST inconvenient.

Like so:
https://imgur.com/a/hRsZcMH

Is one really SOL in this situation?

Sorry that happened. I honestly don't know. Never experimented with that.

One thing though... you're talking about the track name. When you put DP into record it will name the file after the current track name. It won't change the name of the file if you change the track name after you've already recorded audio. So the file name should still be the same if you open up the Soundbites window (Shift+B). If you change a track name and then start recording again, I'm pretty sure DP starts a new audio file named after the new track name.