::::We have definitely always said the Hague, and never just "Hague". But we never said The Hague with a capital The in mid-sentence. That is some bizarre modern Wikipedia hypercorrection. That's like people retroactively putting CamelCase into words where it never existed in the past.
My interest is more in how we used to alphabetize the name. That I do not recall specifically but I suspect it would have been listed under 'H', not 'T', since the the is only a the. Computer sort order didn't use to matter; there was no such thing. People named M', Mac, and Mc were put together in a group by hand by some typesetter.