The word 'marriage' has a stigma attached to it thanks to a lot of people in the world that deem it should be between a man and a woman only.
So taking the idea, the aspect of marriage and that partnership and naming it something else, even though in essence it's the same thing but includes same sex marriage is a way of shedding some of that stigma.
People could argue "Well it's marriage!" And it could be argued that no marriage exists in Eorzea, but handfasting or bonding instead, so they can keep their precious 'straight onry marriage' and cram it somewhere (politely, of course). To answer another part of your question; Yes, the new name would be the equivalent of marriage^^;
Now pair the rename with say... reworking what the bonding actually is - say for instance you leave it up to the player to define what their pact means to them - Whether it's friends swearing allegiance to eachother, or lovers taking vows, each ceremony could be the same regardless of what oath was being sworn, that could sidestep a lot more fallout too because then SE doesn't have to say "We're allowing SSM", they could say "We're allowing players to Bond, or show their allegiance to eachother." Again shedding the whole 'you're screwing with the sanctity of marriage' crap.
I'd love to see more ideas being pushed around guys! It'd be awesome if SE did read this and take note ;~;
Edit: on a re-read I didn't realize how harsh my post was sounding haha, maybe I need to sleep more and work less! My sincerest apologies if this offends anyone, totally not my intention. Have a great day!