What is the ruling of the Sharia on registering a young man under the name of his maternal uncle (administrative registration only) for the necessities of study, employment, and citizenship, knowing that his true lineage to his father is known to everyone, and that this registration does not result in any confusion of lineages or forbidden degrees of kinship, and what are the implications of this in the case of engagement and marriage contract?

If the registration of papers was necessitated by a need, and it was on paper only, then you are excused, Allah willing, and the warning mentioned for one who claims lineage from other than his father does not apply to you; because the warning is specific to one who claims lineage from other than his father out of a desire to elevate himself and conceal his lowliness.

When the excuse ceases, it is obligatory to return the matter to its true state in official papers, and there is no problem with your marriage, as you marry yourself, or you appoint whomever you wish to act on your behalf in accepting the marriage.