Item name: Cold Brew Milk
Cold Brew Milk is filled with chocolate and coffee.
or
The Cold Brew Milk is filled with chocolate and cofee.
Is the article optional in this context?
Item name: Cold Brew Milk
Cold Brew Milk is filled with chocolate and coffee.
or
The Cold Brew Milk is filled with chocolate and cofee.
Is the article optional in this context?
It depends entirely on context. If you're referring to the product in general, then it seems reasonable to disclude the article in that case. However, if, for example, you are referring to a single bottle/carton of this product, then the article would be necessary. I don't think the fact that Cold Brew Milk is a proper noun determines whether or not an article is necessary, although I can't justify this.