asking out of curiosity -- why are you seeking to put a date into your project names, if you don't care which date you use?
If it's just to distinguish between them, in cases where you have duplicate names, I would suggest making sure you use a date that never changes. For example, if your project go-live date frequently changes, your project owner might frequently forget to rename the project. So it might be better in that case to go with project conversion date, or even request date if it comes to that. Just one less thing to forget to do.
In order to help with the duplicate name thing, I'd also recommend you put the date first (e.g. YYMM_Campaign_etc.) so that users who are faced with similar-looking project names can immediately sort the names in a more helpful way.