Strictly speaking, the only personal name of God belonging to Him alone, and the most significant name of God found in the Old Testament (over 5000 times).  Yahweh is the approximate (and likely) pronunciation of the tetragrammaton, the four-letter word YHWH.  When Moses asked what His name was to take back to the Hebrews in Egypt, God replied, “I AM THAT I AM (אֶֽהְיֶ֖ה אֲשֶׁ֣ר אֶֽהְיֶ֑ה ehyeh esher ehyeh): and he said, Thus shall you say to the children of Israel, I AM (אֶֽהְיֶ֖ה, ehyeh, 1st person singular, giving God's declaration of His name) has sent me to you” (Exod 3:14).  Thus God revealed to Moses the very essential meaning of His name as Yahweh (יְהוָ֞ה, Yahweh, 3rd person singular, the response of the people of God, He is).  There is a strong indication that Jesus (or Yeshua, Yahweh is salvation) used this name and its divine implication to apply to himself when he said, “Before Abraham was, I AM” (ἐγὼ εἰμί, egō eimi) (John 8:58).  Thus, the very Person who spoke to Moses out of the burning bush was the very same Person who addressed the startled Jews in the Gospel of John.

For a more complete discussion of the personal name of God, see the passage in Exodus in which He reveals His name to Moses, Exodus 3:14, 15.

This is a generic name for the divine being. In the Hebrew Bible, the word is regularly used in the plural in reference to the God of Israel but in regard to His majesty or intensity. The plural has a third person singular with the God of Israel, but a third plural with foreign deities.

This Aramaic term is used only three times in the NT and approximately 80 times in the writings of the early church fathers when quoting or paraphrasing Jesus’ words. It is translated by the very next word in this verse as ὁ πατήρ (ho pater) “the Father,” as it is in all three NT uses. Jesus spoke in Aramaic, and Hebrew, both languages being used in Israel. In Jesus’ day, abba was used for the father in the family, and was a customary title for God in prayer among the Jews. It was eventually taken over by Greek-speaking Christians as a liturgical formula. Some posit that abba is equivalent to “daddy,” an American English term for “father.” This assumes that the American informality expressed by children toward their father would have an analogy in Jesus’ culture, an assumption difficult to sustain. It is, therefore, not appropriate to refer to God as “daddy.” Linguistically, then, abba means "father" in Hebrew, Greek and English. It must be noted, however, that while “father” is a term of respect in biblical literature, it is also a term of affection, very deep and abiding affection. With His use of “Abba,” Jesus expresses His respectful and intimate relationship with His Heavenly Father in prayer, a wonderful example for all believers.