If you want to be really proper, you would write it in cuneiform, as seen on the first line of this inscription. If you can't write in cuneiform, but you want to get as close as possible in Latin letters, then you would spell it "Nabû-kudurri-uṣur", which is a transliteration of that cuneiform.

All other spellings are derived from this (Nebuchadnezzar, Nebuchadrezzar, etc).

The spelling of names from one language often change as they get adapted into other languages. Not all languages have the same set of sounds, and some letters are distinguished in one language and not another. So unless you are spelling it in the original writing system, you're using some other alternative spelling of the name.

Both modern variants have filtered down to English through Hebrew, so the name has been transliterated twice. If you've ever thrown a sentence into Google Translate and translated it a few times into other languages and then back to English, it comes out signficantly different. The same sort of thing happened to Nebuchadnezzar.

The earliest attestations of it in the Hebrew Bible are in the books of Kings and Chronicles, and use the spelling with an R sound in the middle. The later attestations in the Hebrew Bible (Ezra, Nehemiah, and Daniel) tend to use the spelling with an N sound in the middle. But both are used in the Hebrew text from which we get our spelling, so if it's misspelled in one of them, the misspelling/mispronouncing is over two millennia old.

I think that because Nebuchadnezzar had a bigger part in Daniel's story than in the story of the conquest in Kings and Chronicles, the N spelling has become the more predominant one.

Neither of them are "wrong" per se, it's perfectly fine to use the N spelling. It's been used for 2500 years, after all. The R spelling probably preserves more of the original Akkadian, but both are considered correct.

According to the Oxford English Dictionary it has been spelled just like in your title - Nebuchadnezzar - since the early 20th Century.

However, remember that 'proper' spelling is not set in stone. Especially with proper nouns which come from other languages spellings can change with time, based upon various accepted methods of translation, pronunciation and transliteration.

Moreover, it is also possible for different authorities - such as publishing houses or university departments - to have different style guides which may not agree with each other.

It is also possible for a proper name to have several different variations of spelling which are generally considered acceptable.

So I cited one authority, the OED, but it is very possible to find other authorities which give different spellings. Generally speaking I think the OED is a pretty weighty authority when it comes to the English language.

It is important to understand that words originating from languages that do not use the Latin alphabet do not have strictly "correct" spelling when using the Latin alphabet. That would be impossible.

What they have are phonetic spellings that try to mimic how the word should be pronounced, and there are usually going to be differences of opinion about how that should be accomplished because word sounds in every language do not always match up well with letter usage in the Latin alphabet.

For example, Mohammed and Muhammed are both acceptable ways to spell the Islamic prophet's name. The pronunciation of the second letter is somewhere between a standard o and a standard u sound in English. Originally Muhammed was used more often, and now Mohammed is used more often, so which is the "correct" way. Should you go with the original favorite, the current favorite, or something else entirely?

Sometimes there is a Respected organization that can step in and settle the matter. A governing language body, government, religious authority, or leading association of professionals in a specific field could all agree that one spelling is proper and the rest are improper, or they could just specify a preferred spelling.

So the answer is that you can write it in cuneiform if you want to get it exactly right. You could go with a governing language body and use he version written in the Oxford English Dictionary. You could use a government as your guide and use the version used by the government of Itaq, since that's where he lived, or the government of your own country (US for me) or the government of the country from which your language originated (England). You could try to find the first reference to it in text and go with that, since it was first. You could use the version written in the bible if you think that holds weight for you. You could take an encyclopedia, a scientific paper, or an academic book as a definitive source. You could take a poll of historians and use the version that gets the most votes.

Bottom line is: if it didn't originate in a Latin script, there is no right answer and you can safely use ANY version that was at some point used by any sort of authority as long as it wasn't specifically condemned afterward.