God never tells us when He writes our names in the book of life, only when He blots them out. I believe this is because Christ died for the sins of the whole world, and everyone's names were there in the book until they reject Him.
He said He wished that none would perish, even knowing most would not receive Him. It isn't a matter of when our names were written in the book; it is a matter of whether or not they are blotted out when we refuse to trust in Him, perhaps determined at our death.
Revelation 3:5 "The one who conquers will be clothed thus in white garments, and I will never blot his name out of the book of life. I will confess his name before my Father and before his angels."
All born-again believers are overcomers, because of Christ in them. Those who are not overcomers are those who trusted in themselves and not in Christ. They attempted to "be a Christian" without any desire to be one with Christ.
Everyone is in the book of life until those who reject Christ are blotted out.
Romans 12:2 "2 And do not be conformed to this world, but be transformed by the renewing of your mind, so that you may prove what the will of God is, that which is good and acceptable and perfect."
Psalms 128:1 "1 Blessed is everyone who fears the Lord, who walks in his ways!"
When Christ transforms us into a new creation, there is no going back; it is eternal. Hallelujah!!!!