Should "the" ever be dropped from the beginning of a name/title?

Imagine two places exist, both called The Haunted Forest. How would I specify which forest is being referred? Would one say the northernmost Haunted Forest, or the northernmost The Haunted Forest?

If the is dropped, what is the rule that makes it appropriate to do so, and would it be any different if instead of a place, I referred to, for example, a book title?

The simple answer is that generally you don't use the definite article twice. It's just awkward. One the is enough to define what you're talking about.

If one is referring to the Ashdown Forest*, you don't use "the English The Ashdown Forest" to contrast it with another. It's "the English Ashdown Forest".

Similarly with book titles. The Homecoming is a title of a book by Harold Pinter. It's also a book by Ray Bradbury. But again, it's not "The The Homecoming by Pinter is longer than Bradbury's," it's "The Homecoming by Pinter is longer." Typographical conventions help with book titles of course.

_{*It's quite surprising how many references to "Ashdown Forest" it's possible to find. But one is always "on the Ashdown Forest," not "in Ashdown Forest."}

In the Wikipedia article of The Economist, I found one sentence where "Economist" was not preceded by "the"; everywhere else it was "The Economist".

Similarly, in the article of The Times, I found a sentence where instead of "The Times", "Times" was used.

And now, I have a faint recollection that I have seen "the" being dropped in many similar situations. Thus, you would say, "the first Economist was published in..." rather than "the first The Economist was published in...".

So, in your case, I can safely say that you have to drop "the", and write it as:

...the northernmost Haunted Forest...