The bible tells us what we need in order to be saved:

John 3:16
For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.

John 11:25-26
Jesus said to her, “I am the resurrection and the life. The one who believes in me will live, even though they die; and whoever lives by believing in me will never die. Do you believe this?”

1 John 5:11-12
And this is the testimony: God has given us eternal life, and this life is in his Son. Whoever has the Son has life; whoever does not have the Son of God does not have life.



That is the entirety of the plan of salvation. It is all that it takes to be saved. There are no extra requirements of any kind, this includes any requirement to keep a certain name.


Scripture also goes on to tell us that this is not something that can be taken from us:


John 10:27-30
My sheep listen to my voice; I know them, and they follow me. I give them eternal life, and they shall never perish; no one will snatch them out of my hand. My Father, who has given them to me, is greater than all; no one can snatch them out of my Father’s hand. I and the Father are one.

No legal authority can take away your salvation by changing your name or through any other means.

My guess is that, if the Book of Life exists at all, then God will simply write down every name you will ever be known by in it. God is aware of what names you will go by through all of your life; a name change will not catch him by surprise. But more likely, there really isn't a Book of Life to begin with. The Book of Life was probably a symbol God used to teach us about salvation, predestination, and his knowledge of all things past, present, and future.