This is a false-equivalence. "Milk" is not a trademarked brand name like "Coca Cola" or "ChatGPT", it's a category of food/drink. You can't trademark "milk" in the same way you can't trademark "sausages".
A better comparison would be "Not Cola", which AFAIK would be an acceptable name for a drink. See literally all smaller Cola brands which include the word "Cola" in their name.
A better comparison would be "Not Cola", which AFAIK would be an acceptable name for a drink. See literally all smaller Cola brands which include the word "Cola" in their name.