Originally Posted by Mjölnir
The whole idea Killian had was to play on people's expectations, which makes them easier to trick because they see what they expect to see. The twist works in two ways because it plays the audience a meta level in similar fashion.
The idea was obviously not to just get rid of the Mandarin and the proof for that is the argument you bring up yourself; they wouldn't have had a real Mandarin in the movie in that case.
But there are no grounds for giving Killian the title of Mandarin. It doesn't matter if he's "more like the comicbook version", no character in the movie has read any damn Iron Man comics so the only Mandarin that has been established to them is Kingsley's version. And that version is an entirely different thing than Killian's Mandarin so for a character inside the movie naming Killian "The Mandarin" wouldn't make sense