There is in fact a thing called "collaring ceremony", people who are in or know things about BDSM communities might be familiar with this. It's often compared to a wedding but the couple in question uses a collar for the "submissive" instead.
It's not what Aziraphale and Crowley are doing here(tho you are free to interpret it as such) but I thought I'd mention it because Aziraphale isn't the only one who may think of it as a second wedding band π€ I could imagine that Crowley isn't very familiar with this and perhaps a little flustered about the metaphorical weight Aziraphale places on the object but! I don't think he'd complain about Aziraphale wearing it every once in a while just for fun π