Hi, @mgaplus4! I really like the Scripture you brought up in responding to this question. I love the reassurance these verses give and the reminder that it isn’t by our works that we are saved–but by grace through faith in Christ.
I do believe you are correct in understanding that He will blot out of the book of life those who do not overcome. However, I think that begs the question, what does he mean by overcome? Who is an overcomer? In 12:11, it says “…they overcame him by the blood of the Lamb and by the word of their testimony…” Like the Israelites with the Passover, those who believe in Christ as their Savior-accepting his death and resurrection for their atonement and justification-are covered by his blood. We are overcomers in our confession and belief in Jesus as Lord and Savior. As to the part about overcoming by testimony, Romans 10:8-11: “But what does it say? ‘The word is near you, in your mouth and in your heart’ (that is, the word of faith which we preach): that if you confess with your mouth the Lord Jesus and believe in your heart that God has raised Him from the dead, you will be saved. For with the heart one believes unto righteousness, and with the mouth confession is made unto salvation. For the Scripture says, ‘Whoever believes on Him will not be put to shame.’” (New King James Version). I believe this is to what the Revelation verse refers when it speaks of overcoming. It isn’t speaking of overcoming by our own strength or works (not by might nor by power, but by My Spirit…Zechariah 4:6). Think Cain and Abel
In regard to @Maheshnalluri’s question, I think these verses give us sure security in what Christ has done. It’s only by the blood of Christ and our testimony that we are able to overcome, meaning nothing we ourselves could do-no work of ours-could justify us before God. That faith is credited to us as righteousness. @SeanO gave a great response :).
Let me know your thoughts. I hope this helps at least somewhat.