I never really liked the title software engineer. I didn't think of myself as an engineer. I certainly hadn't had any training as an engineer.
Some dictionary definitions -
While I certainly try to make efficent and economical structures, I don't think a very many scientific and mathematical principles go into it. On the other hand, I am definitely skilled in making, using, and repairing these 'machines' we call software. So I think software mechanic is a better description.
I guess calling myself a software mechanic might be considered a bit precious, but software engineer strikes me as a bit pretentious, and most of the time I still refer to myself as a programmer, or I say "I do software development". I don't squawk too much if whatever company I work for decides to call me a software engineer. They can cling to whatever illusions they want.