שלמה הטוב is a "hidden" member of the Tov family. He is alluded to in the benching (Birkat Hamazon) in the bracha Hatov Vehameitiv, which, incidentally, does mention 3 of his brothers:
ורחמים וחיים ושלום וכל טוב
And Rachamim, and Chaim, and Shalom, and all the Tov's.
Not only is he not mentioned in the Talmud or Bible, but he isn't mentioned in the bracha either. The reason is that he was the best of the "Tov's". Everyone knew it, and he knew it too. He was better than his brothers. For a while, he was singing his own praises about how good he was. His brothers became annoyed, and rightfully so. They wanted to harm him to get him to stop.
His youngest brother, Rachamim, had mercy on him and calmly told him what the problem was. And, he said to Shlomo, "Look, if you just don't mention your name, anywhere, we'll leave you alone." Everyone knows who you are, already because you appear in all these rabbi's private letters that they send each other. You don't have to also be in the Bible or Gemarah, as well. Give your brothers a chance to show off our family heritage."