I’m wondering what is more appropriate when referring to a city, let’s say Damascus for example. Is it better to say “city of Damascus” or “Damascus city”? Or are they both interchangeable. I know for certain cities it is explicitly known, such as “City of Toronto” or “New York City”, but for ones where it simply the city name, what is the convention? Thanks
In Canada, the "City of" formulation usually refers to the municipal government specifically. So a lawn mower or other park maintenance equipment doesn't belong to Toronto, but to the City of Toronto, often just called "the city" by people who live there. It isn't the name of the city, but of the city government.
The main purpose for putting "city" at the end of a name is either that it's in the official name, like Kansas City, or to distinguish it from something else with that name, for example saying New York city because you don't mean the state.
If you just want to refer to the place, not its government, and it doesn't have the word city in its name, then you're free to just call it Toronto or Damascus. You could say "the city of Toronto" just as you can say "the state of Michigan" or "the country of Italy" - but you don't have to. Saying Toronto City would confuse people, I feel.
In Ontario, new cities are occasionally formed through amalgamation, though this has lessened this century. I have watched the transition from "City Of Kawartha Lakes, Ontario" to just plain "Kawartha Lakes, Ontario" - it takes about two decades. If you are writing about an imaginary city that is super new you might want to keep this in mind.
Also for London UK, the City of London is not at all the same as London and does not refer to the municipal government. That's a special case. (Among other things, it's a county in and of itself and is not a borough of the larger London.)