how to get marriage registration done

His wife can give an Affidavit before the Notary that her maternal name is xxxxxxx and after marriage, she is being called as ..............   the same names belongs to her.  If requires her husband may also give an Affidavit regarding his wife's name before marriage and after marriage.  That is sufficient.  For passports, they go for re-registration of marriage.  

Notary affidavit is enough as the children are the live document of their union and moreover when the wife and husband themselves are not disputing their relationship as husband and wife, demanding marriage registration certificate is unreasonable!

The best option is approaching the Registrar of Marriages, as they might have faced such cases in the past, they may guide for providing certificate, providing necessary documentation required for that purpose.   When Voter card, AADHAR , employment documents are available, insisting registration certificate may be redundant.

Approach Registrar of Marriages with proof of Marriage like Subha Lekha (Wedding Invitation), marriage photos and seek their guidance for Registration of Marriage now.

Procedure query.

It is better to consult and engage a local prudent lawyer for proper analyses of facts/ documents, professional advise and necessary proceeding.