I'm not enough of Roman historian to know: but have to imagine that when Roman Christians began using the "Anno Domini," it was intended to differentiate them from their fellow Romans use of the Empire's AUC (anno urbis conditae, "year since the city's founding") dating-system.
A good intent, no doubt, to set themselves apart from "the world" and its ways. But, at least in its English version, "the year of our Lord" has always sounded to me a bit arch, or even combative: "the year of OUR Lord (not yours)."
So I still remember how it forcibly struck me, reading "Pogo" some 60 years ago, when one of cartoonist Walt Kelly's characters referred to "the year of everybody's Lord."
The truth of those words hit me immediately, their spiritually-profound truth...in a newspaper-cartoon !!
Their truth still resonates with me.