Yes.
What does that mean? It means much more than we think it does unless we gain an appreciation for what “name” means in Middle Eastern languages. An expert in the Aramaic language that Jesus spoke tells us that our name is both our unity with all that exists and our unique note in the harmony of the universe, our personal thread in the tapestry of nature.
The word that we call our name in western thinking can be changed several times. In some ancient cultures when infant mortality was high a child was not given a name unless it survived its first year outside the womb. (Hebrews waited eight days.) Then it was given the name of its childhood. Later, at a coming of age ceremony signifying entrance into adulthood, the person was given a name that was appropriate for who they had become. However, the word “shem” which we translate as “name” identifies us in a much deeper way than any outward label. It identifies our unique essence.
So when we say Jesus knows your name, we are saying that Jesus (an important Name itself) knows who you are. Others may call you names that are hurtful, but Jesus knows who you truly are. When God says “I have called you by name, you are mine,” we can understand that to mean that we are in harmony with the universe, that we are in tune with the God who is love and justice, goodness and mercy.
Another implication of this is illustrated in our modern usage of name when we say we have been named to a team. God has named you. That means you have been chosen to play a part in what God is doing. Welcome to the team that is working for goodness in all things.
Does Jesus know your name? Yes. He calls you his beloved.