Let's look at that scripture, ISA 43:10, in context.
Isa 43:10 "'You are my witnesses,' declares Jehovah" is a reminder about what God had done and will do.
Vs 1: God reminds them that he bought them and they belong to him. (Jacob and Israel)
Vs 2: God promises to protect them
Vs 3: God reminds them that Egypt was their ransom
Vs 4: God tells them they are precious in His eyes
Vs 5-7: God assures them of his continued being with them
Vs 8-9: Now, here's the key: God issues a challenge to the nations and asks them to produce THEIR witnesses to see who is right: "Let all the nations assemble in one place,..."
"Let them present their witnesses to prove themselves right"
Vs 10: God then says to the Israelites, "YOU are my witnesses."
This wasn't about naming a group of people. This was about who is right and who is wrong. Who could produce witnesses for themselves that could truthfully claim to have been a saviour, protector, etc.
This was God's challenge to the nations, and He names the Israelites as HIS witnesses to that fact.
Then Isa 62:2 adds "The nations will see your righteousness, O woman, And all kings your glory.
And you will be called by a new name, Which Jehovah's own mouth will designate"
This was fulfilled in Acts 11:26 - "the disciples were by divine providence called Christians."