Yes, it sounds less important without the 'the', but you're looking for The Doon School.
It's not Doon School, it's The Doon School! We have no branches.
An elite all-boys boarding school in northern India (often called the Indian Eton by the press, much to its dismay), which has produced famous politicians, journalists, writers, artists, and, quite often, self-entitled brats who think they run the country. Or they should run the country.
The Doon School governance model has come to an end, and the country is now led by a man of the people.
The Indian literary landscape is infested with the Doon School diaspora.
She's going out with a Doon School boy? My sympathies
An alumnus of the elite Indian boarding school, The Doon School. A contraction of the words "Doon" and "School" (shocking, but true).
We all know self-absorbed and entitled Doscos run India. Remember Rajiv Gandhi?