Neither "Damnation" or any other word form of Damn appears in the King James translation of the Old Testament, but it does appear in the New Testament.
Mostly it's two words translated "Damnation" Krima(2917) and Krisis(2920). Both are elsewhere in the KJV translated Judgment and Condemnation.
Krino(2919), another form of Krima is translated "Damned" in 2 Thessalonians 2:12, it is usually translated things like judge, condemn, decree ect.
The other two occurrences of "Damned" are Katakrino(2632), which means "to judge against" or "Sentence".
In 1 Peter 2:1&3, Apoleia(684) is translated Damnable and Damnation. This word also gets translated Destruction and Perdition, like in the phrase "Son of Perdition" or "Goeth into Perdition" in Revelation about The Beast.
It is only Apoleia that comes close to meaning what most Christians today casually mean by "Damnation". But even then it could mean destruction in a mortal or physical sense and not necessarily an eternal sense.
The K words that all mainly mean judgment are the ones clearly used in direct connection to the concept of going to Gehenna or the Lake of Fire.
Apoleia is rare in the Gospels, used by Judas in Matthew 26:8 and Mark 14:4, the KJV renders it "waste" there. And by Jesus only twice, in Matthew 7:13, the verse about the broad way and the narrow way. And in John 17:12 where he calls Judas the Son of Perdition.
The form of the word used in Revelation is the form that ends with an N. Further backing up in my view that it's similarity to Apollyon is intentional.
Apoleia has also sometimes been translated "Ruin", between that and the "Waste" translation I feel confident that it doesn't inherently mean complete annihilation.
So when you stumble upon this word reading The Bible. Be aware that it might not mean what you assume it means.