What is the ruling on a man marrying under a name other than his real name to obtain residency and citizenship in a European country? What is the ruling on the children resulting from this marriage? Are we sinful for not informing his wife and her family of his real name?

If the marriage contract fulfills its conditions and pillars, then it is valid. Among the conditions is the designation of the spouses. If the husband was known by what distinguishes him from others at the time of the contract, then changing his name does not affect the validity of the marriage. As for attributing the children to the mother's family, if the intention is to attribute them to someone other than their father, then this is an abomination that is impermissible unless a greater harm would result from denying it.