It's common abroad but I don't see it as marginalising to City myself.
Basically, out of Inter and AC, only AC are commonly referred to as just Milan. I know Milan doesn't actually feature in Inter's name but in English they are often referred to as 'Inter Milan' rather than just Milan, like AC are. Does this mean people are disrespecting Inter or implying they are a lesser club? No.
We are City, it would annoy me if we were referred to as just 'Manchester', why would anyone want the club to be referred to as anything except what the people who love the club call it?
And on the plus side, we are THE City now, nobody feels the need to specify Man City and unless it's obviously in the context of a conversation involving the lower leagues or something, people say CITY and it's automatically assumed they are referring to us, both at home and abroad. That's pretty cool.