This is not really an example of unusual circumstances. The reason this sentance needs the word "the" is because you have added the word "company" so "X interior design" is now a modifier of this word. 'Company' is a common noun and usually needs the word 'the'. But if you do not want to use the word "the," it is not always necessary to use the word "company." You could just say "I am proud to be a part of X Interior Design."

I agree with you that there should be "the" in front "X interior company" because it would be a proper noun. Here is an example so you can understand a little better. I am proud to be a member of the X generation. Here X generation is a proper noun. To begin to understand how the is used, we must first think about nouns. All nouns are not the same. To begin with, we can divide all nouns into two large groups: proper nouns, and common nouns. nouns common Proper Proper nouns are names. They are names for people, streets, books, movies, restaurants, countries, rivers, songs, etc. They indicate one specific thing, they point to one and only one example of a type. English proper nouns are always written with the first letter capitalized. Words like John, Japan, Mars, Fifth Avenue, Ginza, etc, are all proper nouns. Proper nouns don't need a the. It's as if they already have one attached, so they can't (except under certain unusual circumstances) take another one. They already mean "the one you know" Common nouns, on the other hand, are general words for types of things. They do not stand for one specific example of a thing, but rather for a class of things, for a type of thing. Words like pencil, boy, river, book, etc, are all concrete common nouns. They can never be used without some form of classifier or article in dialogue. They are all "things" and so we must either know about them beforehand or not.

Are you referring to me?

Surely someone who teaches English should know the answer to this question.