Heidegger's Bible Handbook: Song of Songs: Inscription, Part 2
2. Why is it said to be לִשְׁלֹמֹה, to Solomon?
Now, it is called the Song of Songs (ᾆσμα ᾀσμάτων, the ode of odes, in Greek), which is לִשְׁלֹמֹה, either of Solomon, since it was composed by Solomon under the inspiration of the Spirit of God: or concerning Solomon, the true one, namely, the heavenly, even the Messiah Christ, who, just as He was able to be called דָוִיד/David in Ezekiel 34:23, so also Solomon here; likewise, Solomon was called יְדִידְיָהּ/Jedidiah, the beloved of the Lord, which name in the truth of its substance belongs to Christ. Of course, Christ is also called שַׂר־שָׁלוֹם, the Prince of peace, in Isaiah 9:6.
 2 Samuel 12:24, 25  The name שְׁלֹמִה/Solomon is related to שָׁלוֹם/peace.