The invitation states who officially hosts. When parents are divorced or remarried, the header line gets political: wrong name order can hurt more than a missed guest.
Simple rule: the couple decides. Your names first, then parents who contribute or are close, without forced symmetry if the relationship is strained.
Common wording
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Still-together parents: "Mr. and Mrs. X are delighted to announce the marriage of their children…"
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Separated parents: two distinct lines, or "[Name] and [Name], together with their families…"
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Blended family: name biological parents, optionally current spouse if relations are calm
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Couple-only: "[Name] and [Name] invite you to celebrate…" with no parental line