In North America at least, the term is Professional Engineer. PEs are generally licensed in a way similar to doctors and lawyers. At one point there was a push to professionalize software engineers, but it never got very far.
Feel free to call yourself a software engineer (or even a software doctor). The titles aren’t controlled and as a result don’t really mean anything.
I believe that in Canada, and certainly in Alberta, the titles are very much controlled. The regulatory group APEGA has a Professional Engineer designation for software engineers as well
Context matters. Even in Alberta, the term “software engineer” doesn’t mean anything. Last time I looked into this, Quebec was trying the hardest to control usage and they actually took Microsoft to court for their MCSE title.
Another example: the University of Alberta has a software engineering program.
Search on Canadian job sites and you will find hundreds of software engineering jobs across Canada (including Alberta).
Other examples of non-PE engineers include stationary engineer (people who operate boilers) and locomotive engineer (people who operate trains). They may have their own regulations, but it is entirely distinct from Professional Engineers.
It's a bit complicated. In Oregon, for example, someone was fined $500 in 2015 for referring to themselves an engineer; although they had an engineering degree, they were not a licensed professional engineer. The state law was invalidated in 2018.
Feel free to call yourself a software engineer (or even a software doctor). The titles aren’t controlled and as a result don’t really mean anything.