Adonai is actually not the formal name of God that the Jewish faith refuses to say, out of respect for His name. Adonai is actually the name for the Lord that the Jewish faith substitutes for the name revealed to Moses at the burning bush. What we have in the book of Exodus is simply the Hebrew letters that transliterate as YHWH (often anglicized as Yahweh, but we literally aren't sure how it would have been pronounced as the vowel points have been lost to time). Another word, Jehovah, was the rough mixing of the consonants from YHWH (JHVH) and the vowels from Adonai. Jehovah is not a "real" word but has been used as the "name" of the Lord.
Y'all are all good using Adonai.