How do I make sure my name is in the book of life?
Your name is already written in the Lamb's Book of Life if you have truly believed on Jesus, but Scripture warns it can be blotted out, so you keep it there by overcoming, examining yourself, and living a holy, surrendered life to the end.
The Book of Life is described as a register in which the names of all who will receive eternal life were written before the foundation of the world. Philippians 4:3 speaks of fellow laborers "whose names are in the book of life," and this was true of believers even before the Lord's death on the cross. So the starting point is simple: believing on Jesus Christ is what gets your name recorded, because eternal life is found only in the Son.
However, having your name written there is not the end of the matter. Revelation 3:5 promises that the one who overcomes will be clothed in white and will not have his name blotted out of the book of life, which shows plainly that names can be removed. Revelation 20:15 warns that whoever is not found written in the book of life is cast into the lake of fire, and there is a sobering reminder that some who have been saved can still perish eternally, with their names blotted out. This means simple belief at one point in time is not enough on its own; ongoing faithfulness matters.
Jesus described the path to life as a narrow gate and a narrow way, and said few find it, while the broad way leads to destruction (Matthew 7:13-14). Because of this, you are called to examine yourself seriously: are you truly in the faith, is the Holy Spirit really leading your words and actions, and can you honestly say all is well with your soul? Quick anger, unforgiveness, and offenses left unrepented are the kinds of things that can pull a person off the narrow way, so ongoing repentance and genuine faith, not mere belief, are what keep you walking toward life.
Ultimately, keeping your name secure in the Book of Life comes down to where your treasure lies. If your heart treasures the things of God and you live holy before Him, you walk upright and gain eternal life with Christ; if your heart treasures the things of this world, that pursuit leads to separation from God. So staying in the Book of Life means continuing to believe, continuing to overcome, and continuing to live a surrendered, holy life all the way through.
The scriptures
And I intreat thee also, true yokefellow, help those women which laboured with me in the gospel, with Clement also, and with other my fellowlabourers, whose names are in the book of life.
He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels.
And whosoever was not found written in the book of life was cast into the lake of fire.
Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat: Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.
From the books
This answer is drawn from these passages in the Mary Banks Faith Library.