Facing issue for applying government jobs

There will not be any problem. She has to get the marriage certificate. When she is applying she should write her name as per the SSC certificate. You can change her name in PAN and Aadhar etc. But in education certificates you need not change.

If you have got a marriage certificate then it is all right otherwise get a marriage certificate from the SDM/ ADM office following the standard procedure and once you get the marriage certificate, attach a copy of the same with your wife's application so that the change in the surname is justified and clearly understandable.

It is good that she has your surname in the PAN and Aadhar card which will be very useful at this juncture for her identification.

So she does not need any change in her educational certificates as the marriage certificate will explain the things.

So far as Government recruitment examinations are concerned, I can assure you that your wife won't face any problem. She can write her name as 'Jyoti Agarwal' (nee Gupta) and submit a copy of the marriage invitation card or a copy of marriage registration certificate along with other certificates. There will be no problem on this account.

However, to avoid difficulty in some other cases, your wife can sign an affidavit before a Magistrate in your city. She can publish two advertisements in two newspapers also. The wording will be like this: I, Jyoti Agarwal, hereby declare that I have changed my name from Jyoti Gupta to Jyoti Agarwal after my marriage with Prashant Agarwal. From now, I will be known as Mrs. Jyoti Agarwal'. The affidavit and original advertisements must be preserved permanently

There is nothing to worry. This is a completely normal procedure for ladies after their marriage.

Once a lady enters into a marriage - contract, her educational certificates retaining her surname need not be changed but a marriage - certificate issued by SDM/ADM would be enough to justify the changed situation.
In case, she opts for a job after her marriage, she can apply with confidence and in no way, she will face any issue as a result of her marriage with her husband having different title as his surname.
However, wife can approach a lawyer for the initiation of the affidavit and once the affidavit is accomplished with the signature of the first class magistrate. This needs to advertised in a local news paper apart from the leading English Newspaper for the wide publicity of your affidavit. This cutting is to be preserved in order to produce the same during the process of document verification by the appropriate officials.

In our society and even in many societies world over it is customary to change the surname of the girl to that of the bridegroom to whom she is getting married.

Due to this traditional cultural thing what is required is only a marriage certificate as the proof of the marriage which is sufficient to explain the change in the surname between the educational certificates and the identity documents acquired after the marriage.

If you are not having the marriage certificate then get it immediately from the designated office in your district. Generally it is issued from the marriage registrar office or Sub Divisional magistrate's office. You have to apply for it with the proof of your marriage like invitation card or a physical witness preferably an executive rank person or gazetted officer.

No, there won't be any problem, but she needs to apply for the jobs with her current surname and add the (nee maiden surname together) everywhere she needs to fill her full name. Along with all other certificates, she will have to submit copies of marriage certificate as a proof of identity.
In addition to this, try to build up more identity proofs, like Voter Id card, Aadhar Card and Passport if possible. The Passport will be another proof that she has changed from her maiden name to the post marital surname.