In most of India, a [something] name means a name commonly used by people called [something] by the people doing the discussion, and not commonly used by others except in imitation. For example, if I told you a name was Bengali, I would mean that it is a name commonly used by people who you and I called Bengali, and not much by others. Note that the class referred to are not necessarily people who call themselves Bengali, except in so far as that coincides with who we (you and I) call Bengali.
The `you' is of course the general we on this board.
In any case, the name need not be, and often is not, derived in the Bengali language. So, I disagree with your claim that it should refer to the language: English national adjectives simply do not work that way. A Spanish language name is simply called that: whereas a Spanish name is the name of a Spanish person. So, all depends on what we commonly call Spanish, and the force of my example depends on whether most people would consider a Spanish Basques as Spanish.
We enter a political debate whether we should: but, I believed that they are indeed considered Spanish by most of the world today.
In any case, we should probably take this discussion to the lounge. As far as the record here is concerned, let me leave it at an unqualified apology for having caused hurt.