I think it is much more important that children hear their names mentioned in the ceremony, than it is that they play any major part of the ceremony. (There will be exceptions to this so clear it ahead of time with the shy ones). Mentioning a child's name during the wedding assures that they are an important part of the occasion and have special status which guests and other family members attending do not. At this special time children need to feel important to their parents.
Remember with this ceremony a new family is being born. This is especially important to young ones. When children are coming into the marriage, it is appropriate to mention in the ceremony that not only is a marriage being formed, but also a family - and then we name each child. If a prayer is in the ceremony, each child's name can be stated in the prayer.
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