grammar - Adjective with proper noun

Rephrasing the entire question:

Do we use the article "the" when we use an adjective with a proper noun? Which of these is correct, and why?

The terrible Mr. Brown set my boat on fire.

Terrible Mr. Brown set my boat on fire.

The US-based Galacto, Inc., takes care of its customers.

US-based Galacto, Inc., takes care of its customers.

Do we use the article "the" when we use an adjective with a proper noun? Which of these is correct?

The Switzerland-based ABC Fund operates in most countries of the EU.

Switzerland-based ABC Fund operates in most countries of the EU.

I have a feeling the first sentence is correct but that it sounds a little old-fashioned.
What about phrases like, "The terrible Mr Brown"? You could argue that we're actually saying, "The terrible man Mr Brown". Said like that it sounds like an appositive, but is there something else going on here? Is there a term for this kind of phrase?

EDIT: By using the noun fund in my example, I have not made it clear what the question is. How would "the" work in "The US-based XYZ, Inc."?

Answer

I believe both of these sentences are correct, but that they convey slightly different shades of meaning.

Terrible Mr. Brown set my boat on
fire.

Mr. Brown set my boat on fire; I think he's terrible.

The terrible Mr. Brown set my boat on
fire.

Mr. Brown, who is infamous in these parts for being terrible, set my boat on fire.

When the adjective is "US-based" rather than "terrible", there is really very little difference in meaning between the two sentences. Putting "the" in might make the company sound a little more well-known.