Prosopology is a fancy word that means studying a text to see who the main characters are. Ancient manuscripts did not have all the easy paragraph breaks we do. In the case of the Bible, it uses far fewer proper nouns than we do as well. So that makes it tough to identify who is speaking.
For example, Jesus in Matthew 22 identifies two speakers in Psalm 110 as Christ and the Father (or God). He also identifies David as the author and the Holy Spirit as the inspiring agent.
This is a basic hermeneutical approach to Scripture. Everyone, I think, before the last hundred or so years would have agreed—with some nuance I am sure; and yes, I’d guess the 1800s would have some disagreements as well.
But as Michael Haykin recently noted, prosopology is an important way to read the Bible because, as I argue, it helps you to understand what it means by what it says.
Some shy away from prosopology today. I am not sure why. It does not require, for example, an allegorical reading of Song of Songs. It is a tool to help you grasp the meaning of the Bible.
Yet just as Hosea and Hagar are real people but also signify God and Israel, so it’s possible that Solomon and the Shunammite can be real people who also signify God and his people. And prosopology would be one way to help you ask the right questions of the text to get what the Spirit has for us.