If I won 3rd place or an honorable mention for Award X. Is it reasonable to simply state the name of the award without stating what place I got?
I do not think it is reasonable. If you are mentioning you won at a competition, you must also mention what was your place or in what capacity you won an award. There are good reasons for this in my opinion. First, it is possible the reader is aware of the competition and finds it misleading of you. Second, if you clearly mention the details of the award, it is possible you might rise in the eyes of reader for your integrity and honesty.