Wasted Laurels ~ Double Ascended
I use the name Barbie on all of my characters.
That is what the “Unique” tag means on the items. Other MMOs set this precedent. Anything “Unique” means you can only wear one of them. You are correct it has not been explained in GW2 anywhere.
So it isn’t a complete loss, I believe you can infuse one of them in the Mystic Forge (takes mats from running fractals) and then wear both since the infused version does not count as the same ring. You can also trade it to another character to use. If you have already soulbound both of them then infusing one will make it account bound again so you can trade it.