I want to try to explain some more what I think I'm seeing, and why I don't like it. It might not really be what it looks like to me, and there might not really be anything wrong with it. The way I feel about it is like the way I might feel about someone who never fights fires wearing a firefighter's uniform and calling himself a firefighter, letting people think that he's a person who fights fires. The name "Buddhism" comes from communities whose ways of life, and the benefits that people have found in immersing themselves in them, have given that name the appeal and the social status that it has in some circles. If a person who sees no value in those communities or their ways of life, or worse, views them contemptuously, picks out some of the parts of their beliefs and practices that don't inconvenience him in any way, to wear as a costume over his own personal philosophy and lifestyle, and calls himself by their name as if he is one of them, that looks disrespectful to me, and even dishonest if the person is doing it to enhance his image with some people.
I see another possibility. A person might see some correspondences between his personal philosophy and lifestyle, and some of the beliefs and practices of a religion, and identify with it for that reason. Even so, it still seems disrespectful and dishonest for a person to wear that name without being part of one of those communities, and without making that clear.