As for names, I've seen:
Bonding, Soulbond, Pairing, Pact come up, I mentioned handfasting (Which if memory serves me well originated in ancient Europe and involved tying the hands of the couple together to show a permanent bond)
I'm totally open to new name ideas, feel free to think of some if you can and add them to this thread!
Also good luck on your r/l wedding Twiddle!