I enjoy using Power Query "M" language (Microsoft Reference)
Is this language permitted - and in cases where the language name is to be used, should this be referred to as
Power Query M Language or something else?
As long as the language you mean to use falls into PPCG's definition of a programming language, you're free to use it.
As Nathan pointed out, PPCG doesn't even require you to answer in a programming language, so yes, feel free to use whatever language you like.
Regarding what you should call it, there's no specific answer to that. As Pavel suggested, you can just use the name you feel is appropriate and link to the language's official page.