And BCE is "Before Current era."
Yes, they even took Christ out of our timelines now.
And so when does CE begin? I didn’t get the memo that we changed the convention of year designation.
If the Birth of Christ is the reference, "Common" doesn't work: there are other timelines and year references (Islamic, Jewish, Japanese, Nepalese, Chinese, to name a few, especially noted dating coins), so it isn't completely "common", after all, except in modern usage.
If you're doing archaeology, it doesn't hurt to preserve the history of the timeline, too. Anno Domini (in the year of Our Lord) 2016, for instance.