Why?

The English word 'marriage' is not the one that was used by Christ. Who cares what it's called? Are you going then to make every married atheist suddenly change their status to 'Civil Unioned' or something? You'd have to or it would be discrimination.

And keep in mind that the legal part of this arrangement would probably still be called marriage - it's too enshrined in law to easily and practically change.

I expect if there were to be a name change it would be the churches who would have to change the name of their tradition or some such. Maybe in a Christian church it could be called 'Sacramental marriage' or such like. Indicating sponsored by both church and state.