Hindu marriage Act provides for the registration of an already solemnized marriage. Parties to the marriage have to apply to the Registrar in whose jurisdiction the marriage is solemnized or to the Registrar in whose jurisdiction either party to the marriage has been residing for at least six months immediately preceding the date of marriage. Both the parties have to appear before the Registrar along with their parents or guardians or other witnesses within one month from the date of marriage. There is a provision for condonation of delay upto 5 years by the Registrar and thereafter by the District Registrar concerned.
If there are mistakes in the name of your wife, please get them corrected from where you took the marriage certificate by showing doucmentary evidence.