Is 憨豆先生 (Mr. Bean) commonly used to refer to Rowan Atkinson even when he's playing other characters, or when he's not acting?
No and yes. 

No, because he is "officially" known as 罗温·艾金森. Some of my Chinese colleagues recognized this name, though they couldn't write it (same with me: I am a Ukrainian, and I don't know his name, but I can recognize it once I see it in writing).

Yes, because like in most parts of the world (particularly my home country Ukraine), he is most known by his character "Mr. Bean". Therefore most of my Chinese colleagues could not recognize his official name at all, unless I told them 憨豆先生 or showed his photo.