The verse you are referring to is Psalm 110:1, “A Psalm of David. The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.” Notice in this verse that the first use of the word LORD is capitalized, while the second time, it is not.  There is a reason for this.  In the KJV, whenever we see the word LORD written, that is in reference to “the self-Existent or Eternal Jehovah.”  In the KJV, whenever we see the word Lord (Adonai) written, that is in reference to “the sovereign, i.e. controller:—lord, master, owner”.  The word LORD (Jehovah) is used 5521 times in the Old Testament.  The word Lord (Adonai) is used 287 times in the Old Testament. 

The first time the word LORD (Jehovah) is used in the Bible is in Genesis 2:4, “These are the generations of the heavens and of the earth when they were created, in the day that the LORD God made the earth and the heavens.”  The word “God” is also used here.  It is from the Hebrew word, ʼĕlôhîym, and is in reference to “the supreme God.”  This is a plural word, which gives us a hint as to the Triune God that we serve.  We find this word in the very first verse in the Bible.  Genesis 1:1 tells us, “In the beginning God created the heaven and the earth.”  This word is used 2249 times in the Old Testament.  Often, the word LORD is paired with the word God…the LORD God.

I think it would be helpful to look at this verse in the Amplified Bible which says, “The Lord (Father) says to my Lord (the Messiah, His Son), “Sit at My right hand until I make Your enemies a footstool for Your feet [subjugating them into complete submission].”  This Davidic psalm is so amazing for it is as if David heard Jehovah speaking to Adonai.  One writer defined the intent of this verse as, “God the Father said to God the Son, whom I honour as my Lord, and adore as my God, Sit thou (namely, after thy sufferings upon earth) at my right hand.”  Imagine witnessing this precious dialogue between God the Father and God the Son. 

We are further witnesses of this dialogue between the Father and the Son in Hebrews 1:8, “But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom.”  We know from the first verse of this book that God is being referenced as the speaker.  Jehovah is a Hebrew word and is not found in the New Testament.  The word ‘God’ used here is the word ‘theós’ and means “the supreme divinity.”  In this portion, He addresses His Son, and refers to Him as God when He said, “Thy throne, O God, is for ever and ever…”  The word ‘God’ here is the same word used in verse one.  So, we find God calling His Son, God.  What an overwhelming commentary that proves that the Lord Jesus is God!

Let’s continue by reading verses 9-13, “Thou hast loved righteousness, and hated iniquity; therefore God, even thy God, hath anointed thee with the oil of gladness above thy fellows. And, Thou, Lord, in the beginning hast laid the foundation of the earth; and the heavens are the works of thine hands: They shall perish; but thou remainest; and they all shall wax old as doth a garment; And as a vesture shalt thou fold them up, and they shall be changed: but thou art the same, and thy years shall not fail. But to which of the angels said he at any time, Sit on my right hand, until I make thine enemies thy footstool?”

It is to the Son that God proclaims, “Sit on my right hand, until I make thine enemies thy footstool.”  This certainly helps give an answer to your good question, “Who is YHWH and Who is “my Lord”?  In this portion, YHWH (Jehovah) is God the Father, and my Lord is God the Son.  Psalm 110:1 was a prophetic statement that shows the rest the Lord Jesus entered into when He finished His work on Calvary.  We read in Acts 2:32-36 (which is in reference to Psalm 110:1), “This Jesus hath God raised up, whereof we all are witnesses. Therefore being by the right hand of God exalted, and having received of the Father the promise of the Holy Ghost, he hath shed forth this, which ye now see and hear. For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand, Until I make thy foes thy footstool. Therefore let all the house of Israel know assuredly, that God hath made that same Jesus, whom ye have crucified, both Lord and Christ.”  I trust that you have received the crucified and risen Christ as your savior.  (CC)  (679.4)