Chazal discuss David's language and the balance between intimacy and reverence in prayer and address before God. This sugya is useful for understanding why biblical figures may use different forms of address than later fixed liturgical formulas.
אָמַר רַב יְהוּדָה אָמַר רַב: לְעוֹלָם אַל יָבִיא אָדָם עַצְמוֹ לִידֵי נִסָּיוֹן, שֶׁהֲרֵי דָּוִד מֶלֶךְ יִשְׂרָאֵל הֵבִיא עַצְמוֹ לִידֵי נִסָּיוֹן וְנִכְשָׁל. אָמַר לְפָנָיו: רִבּוֹנוֹ שֶׁל עוֹלָם, מִפְּנֵי מָה אוֹמְרִים ״אֱלֹהֵי אַבְרָהָם, אֱלֹהֵי יִצְחָק וֵאלֹהֵי יַעֲקֹב״, וְאֵין אוֹמְרִים ״אֱלֹהֵי דָוִד״? אָמַר: אִינְהוּ מִינְּסוּ לִי וְאַתְּ לָא מִינַּסֵּית לִי. אָמַר לְפָנָיו: רִבּוֹנוֹ שֶׁל עוֹלָם, בְּחָנֵנִי וְנַסֵּנִי, שֶׁנֶּאֱמַר: ״בְּחָנֵנִי ה׳ וְנַסֵּנִי וְגוֹ׳״.
§ Apropos Ahithophel, the Gemara relates the events that led to his death. Rav Yehuda says that Rav says: A person should never bring himself to undergo an ordeal, as David, king of Israel, brought himself to undergo an ordeal and failed. David said before God: Master of the Universe, for what reason does one say in prayer: God of Abraham, God of Isaac, and God of Jacob, and one does not say: God of David? God said to David: They have undergone ordeals before Me, and you have not undergone an ordeal before Me. David said before Him: Examine me and subject me to an ordeal, as it is stated: “Examine me, Lord, and subject me to an ordeal; try my kidneys and my heart” (Psalms 26:2).