Many years ago my wife had her first name misspelled, we did nothing (we didn't even catch it), and we flew with no problem. We only knew it after the fact when I look at her boarding pass again.
Few years ago my colleague had his last name misspelled (Chen instead of Chan), at first the check-in agent can't find his ticket, then she tried Chen instead of Chan and found it, and let him fly anyway since she knew Chen and Chan are the same in Chinese and it's an honest mistake.
Not sure how bad your misspelling is, but just these two examples show that they are pretty flexible with name misspellings....