What is the Sharia ruling on how to deal with children who do not know about their real father after the father's death and the mother's remarriage, and how can they be informed of this, especially since they are registered under the name of their maternal uncle?

If the marriage was contracted with the fulfillment of the conditions of validity (guardian and witnesses), then the lack of documentation of the contract is not a condition for its validity, though documentation is preferable to safeguard rights. Children are attributed to their father, and changing their lineage is a prohibited adoption in Islam. The lineage must be restored to its true state so that the children know their real lineage, as rights such as kinship ties depend on it, and to avoid the mixing of lineages and the loss of inheritance rights.