Meaning and Derivation: Adonai is the verbal parallel to Yahweh and Jehovah. Adonai is plural; the singular is adon. In reference to God the plural Adonai is used. When the singular adon is used, it usually refers to a human lord. Adon is used 215 times to refer to men. Occasionally in Scripture and predominantly in the Psalms, the singular adon is used to refer to God as well (cf. Exodus 34:23). To avoid contravening the commandment “Thou shalt not take the name of the LORD thy God in vain” (Exodus 20:7), sometimes Adonai was used as a substitute for Yahweh(YHWH). Adonai can be translated literally as, “my lords’ ” (both plural and possessive). Source BLB.org

I find it disrespectful when children call their parents by their given names. I do not allow my children to call me Larry. I set the rules for my children. Perhaps Exodus 20:7 was God’s way of setting that rule for His children, perhaps.

In many states grandparents are given affectionate names to be used with respect and affection. When both grandparents are still living different names are given to each to distinguish the maternal or paternal heritage. The issue is not so much what those names are but rather the loving respect given in the heart of the child.

In many ways I view Adonai as being just that, a loving and respectful name that is heart felt by the children of God.

Galatians 4:6 And because ye are sons, God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.

Being adopted our heartfelt Abba is our equivalent to Adonai.

Abba has the Greek interpretation subjoined to it; this is apparently to be explained by the fact that the Chaldean word, through frequent use in prayer, gradually acquired the nature of a most sacred proper name, to which the Greek-speaking Jews added the appellative from their own tongue, respecting its accent. Source BLB.org