I prefer the title Developer to Engineer because it conveys the iterative work that is a large element of writing most software.
It often is exactly that. I'm probably being too pedantic, but as a developer I don't allow myself to be called an engineer, though some companies have wanted me to. I'm not one, I don't have an engineering degree nor certification and I feel it cheapens the Engineering profession to allow that.
I guess I could be called a "scientist" since I do have a CS degree, but that just feels weird.
I'm a guy who programs computers and runs a little software business. No need to go adding silly titles to that (and if I did, I'd probably go with CEO anyway, since it's quicker to write.)