For clients of particular type only public method names matters. There is no need to suggest Async suffix for private methods. For example I have public methods which checks for arguments or states and throws exceptions immediately (these methods don't have 'async' keyword for 'fail-fast' reasons). And these methods delegate actual work to some private methods like "DoSomeActionInternal" or something like that. These method are hidden from outer client so it's pretty annoying to have suffix suggestions.
It would be nice to have some settings to turn off these suggestions for private methods.