There are three words in the Greek that are translated to English as "hell". There is "Hades" which is translated from the Hebrew "Sheol" which means "the grave".
There is the Hebrew "Gehena" or "Geena of fire" which is a reference to the garbage pit outside of Jerusalem which is a transliteration of the Hebrew "Gai Hinnom", or "The Valley of [the sons of] Hinnom"
Then there is the Greek "Tartaroo" which means "to thrust down to Tartarus". It is only found in one of Peter's letters. Homer describes it as the prison of the Titans, or giants which is not all that different than the biblical "Rephaim", or those spirits who sinned during the days of Noah.
Christians tend to conflate all of these differing terms.
Perhaps we can debate about the term "Hell", but it's undeniable that the Bible uses an actual description instead of just one term to talk about Hell. It mentions a Lake of Fire where beings will be tortured forever (Revelations 20:10).
No, the lake of fire is not hell. We know this from verse 14 where it states:
And death and hell were cast into the lake of fire.
Hell is not the lake of fire. Hell is thrown into the lake of fire. This only makes sense if the word "hell" is referring to the grave. Death and the grave are thrown into the lake of fire. Do you think death and the grave are going to be tormented forever in the lake of fire?
We have the author's definition to help us understand what he's actually talking about. He points out that to be thrown into the lake of fire is actually the second death. Unless death has some other definition which is commonly understood and accepted to mean eternal life, it doesn't make much sense to assume a second death means the exact opposite of what it is commonly accepted to mean. Death means the end of life, right?
Moreover, it is only after everyone has been judged that death is destroyed We know this from Paul's comment:
1 Corinthians 15:26 26The last enemy that shall be destroyed is death.
If death were thrown into the lake of fire FIRST, and then everyone else who was judged to the lake of fire, it would stand to reason that they would suffer forever due to the fact that death had already been obliterated in the lake of fire. This isn't the case though.
Whether or not we call this Hell is a moot point,
Not really. You're conflating these two terms which only causes confusion.
because the description "tortured forever and ever" points to eternal punishment either way.
Not really. As I pointed out earlier, death and the grave aren't exactly sentient beings. The author is exaggerating to make a point. We live in a world where loved one's suffer and die, and we suffer at the loss of our loved ones. The author is showing that at some point, the tables will be turned and instead of us suffering, it will be death and the grave personified that will be tormented forever.