A wedding anniversary is the couple's. The available rites, the year-themed gift tradition, and the family conventions are tools the couple may choose; none of them are required, and the day is honored equally whether marked publicly with a vow-renewal service or privately between the spouses. The pattern across Christian traditions is the same: the marriage itself is the principal observance, and the rites and conventions are supports.
Some anniversaries are difficult. A widow or widower marking what would have been an anniversary; a divorced person observing the original wedding date; a couple in a hard year of illness or family loss; adult children remembering a parent's anniversary after divorce. The Christian traditions do not formally rite these moments, but the day still matters and pastoral acknowledgment is normally available. The couple's pastor or priest is the conversational resource where the day is complicated; a Mass intention, a private prayer, or a conversation can mark what the public form cannot.