When you have something you do not want to forget, do you write it on your hand? Some people write things on the palms of their hands; others write things on the back; others don't do this at all.
In Isaiah 49, God is reassuring his people in exile that his purposes for them still stand. In verses 1-7, God promises that his servant will redeem not only Israel, but people from one end of the earth to the other. In verses 8-13, God tells them of the consequences of this: They will be redeemed, comforted, brought out of their captivity. Of course, both those sets of promises are most gloriously fulfilled in the finished work of Jesus.
But then God anticipates an objection, and proceeds to answer it. Here's Isaiah 49:14-16:
But Zion said, ‘The Lord has forsaken me,
the Lord has forgotten me.’
‘Can a mother forget the baby at her breast
and have no compassion on the child she has borne?
Though she may forget,
I will not forget you!
See, I have engraved you on the palms of my hands;
your walls are ever before me.
Maybe you write on your hand not to forget to pick up some milk on the way home.
Isaiah 49:16 is an anthropomorphism: God does not have hands, (although Jesus does, according to his human nature). But for the sake of communicating something precious, let's suppose he does. What does God write on his hands? What does he want to make sure he will never forget?
The answer is: The name of his people. Your name, if you are a Christian. You can be absolutely sure that he will not forget you.
We need to be a little careful not to individualise this too quickly. The Hebrew for "you" is feminine singular. He's speaking of Zion / Israel collectively. In the new covenant era, this speaks of the Lord Jesus, the one who embodies God's servant Israel. But it also speaks of all those who are in Christ, and so we Christians are included in the people God will never forget.
Which means that, if you are a Christian, this is a picture of how God will never forget you. He won't forget you because you are part of the people whose name he has indelibly written on his hands. It's a most beautiful picture, designed to give God's people (down the ages) complete reassurance: Their God will never, ever forget them.