I've said before that I think that the benefits and responsibilities that we associate with "marriage" should more objectively be associated with "family". My grandfather and his elderly sister lived together (with my uncle) for decades after their spouses died. There was nothing sexual going on, but they were a family as much as any other. Why shouldn't they have been able to file a joint return or claim all of the other benefits of married couples?
Fixing that wouldn't involve abolishing the civil term "marriage", it would involve instead more formally defining "family" and adjusting the legal code as appropriate.
I think "marriage" is a perfectly good term and there's no reason to give it up. Those who have no religion should not have to give up the term, either.
Finally, I think there is less chance of disruption in applying a broader interpretation of "marriage" than in eliminating the term. I don't think that giving in to those who say "no marriage for you!" is a good solution because, as you say, it's not the word that really matters. They would (and they will) find another "tradition" on which to hang their ideology of excluding those who are different.
FWIW.
Cheers,
Scott.