I concur.
If your name is written in the Book of Life, how is it possible that it can be blotted out?
Revelation 3:5
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.
In other words, if you don't overcome your name can be blotted out of the Book of Life and your name will not be confessed to Father.
Exodus 32:33
And the LORD said unto Moses, Whosoever hath sinned against me, him will I blot out of my book.
It is clear from Scripture that you can indeed have your name blotted out from under Heaven.