"We need not decide in this case whether the name "marriage" is invariably a core element of the state constitutional right to marry so that the state would violate a couple’s constitutional right even if — perhaps in order to emphasize and clarify that this civil institution is distinct from the religious institution of marriage — the state were to assign a name other than marriage as the official designation of the formal family relationship for all couples.  Under the current statutes, the state has not revised the name of the official family relationship for all couples, but rather has drawn a distinction between the name for the official family relationship of opposite-sex couples (marriage) and that for same-sex couples (domestic partnership)."

They followed this statement with the holding that same sex couples are entitled to the dignity and respect accorded to "officially recognized families" and that the state could not assign a different designation to them.

The very subtle suggestion here is that the legislature could come up with a different name for this institution ---perhaps-- but that it would not pass constitutional muster unless same sex couples had a right to enter into this officially recognized family unit as well.

This appears to be inspired by the way "marriage" is handled in Mexico and France for example: It's a civil institution and the religious ceremony is legally irrelevant. Absolutely irrelevant. In fact, marriage in the church does not accord you legal protections.