That is the meaning of the verse. The Father speaking to the Son, Jesus took up His throne at the right hand of His Father.
The Greek word kyrios is used for both the Tetragrammaton and as a literal translation of adonay, "lord" "master". So Psalm 110 uses kyrios twice, the first for YHWH and the second for Adonay.
Jesus is YHWH, because His Father is YHWH. Jesus is Adonay, because His Father is Adonay.
So when Paul says in Philippians 2 that every knee will bow and every tongue confess that Jesus Christ is Lord (kyrios) it's not an accident that this looks like what was written by the Prophet Isaiah,
"Speak up and present your case--yes, let them take counsel together. Who foretold this long ago? Who announced it from ancient times? Was it not I, YHWH? There is no other God but Me, a righteous God and Savior; there is none but Me. Turn to Me and be saved, all the ends of the earth; for I am God, and there is no other. By Myself I have sworn, truth has gone out from My mouth, a word that will not be revoked: Every knee will bow before Me, and every tongue will swear. Surely they will say of Me, 'In YHWH alone is righteousness and strength.' All who rage against Him will come to Him and be put to shame. In YHWH all the descendants of Israel will be justified and will exult." - Isaiah 45:21-25
It's almost impossible to look at this passage in Isaiah and what Paul says in Philippians 2 and not see how Paul is intentionally using this passage in Isaiah. When Paul says that every knee will bow and every tongue confess that Jesus Christ is Lord, it is almost explicit in what is going on here. Jesus Christ is YHWH.
Or look how elsewhere in the New Testament we see things like how there is no other name other than the name of Jesus Christ by which anyone can be saved, there is no other Lord, no other Savior. Jesus Christ is not another other than YHWH, Jesus Christ is YHWH.
Jesus Christ, as God the Son, is YHWH, even as the Father is YHWH.
For here are two statements which are true:
"Hear O Israel, YHWH our God, YHWH is one" -Deuteronomy 6:4
"We worship one God in Trinity, and Trinity in Unity, neither confusing the Persons, nor dividing the Substance." - the Athanasian Creed
-CryptoLutheran