Question: Galatians 3:28 states, "There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for you are all one in Christ Jesus."Does this mean we should have the same name or respect all person’s choice of a name?
Answer: If you go back to Galatians 3:26,
"For ye are all the children of God by faith in Christ Jesus." - Galatians 3:26
...you will see that only those who have put their faith in Jesus Christ are the children of God. This agrees perfectly with John 1:12. Therefore, we are all "one"; that is, everyone who has their faith in Christ is a child of God. This is our position in Christ, which will never change; because, you can never lose your salvation or sonship. (John 10:27-29).
Galatians 3:27 is spiritual baptism. When we trust Christ as our Savior, we are placed into the Spiritual Body of Christ. (1 Corinthians 12:13). Remember a very simple principle with reference to baptism. Whenever you find "baptism into Christ or His Body," it is always spiritual baptism. When you find "baptism unto Christ’s death," it is water baptism.
"For as many of you as have been baptized into Christ have put on Christ." - Galatians 3:27
Now for Galatians 3:28, the verse in question.
"There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus." - Galatians 3:28
From Revelation 2:17 and 3:12, many scholars believe that each Christian will have a new name of identification in Heaven. This will go along with everything else that will be new to them, including a new resurrected body. (Philippians 3:20,21).
Most importantly, in reference to Galatians 3:28, notice Acts 10:34.
"...Of a truth I perceive that God is no respecter of persons."
In other words, no matter what your nationality, position in society, or your sex; when you put your faith in Christ you are all ONE. That is, all are a child of God, all are a part of the Body of Christ. In John 3:16, "God so loved the WORLD," showing He is no respecter of persons.