To add the surname "Kashyap" to your deceased father's name in a Central Government employee service record, you will need to follow a formal procedure. This process is governed by the rules laid out by the Department of Personnel and Training (DoPT).Since your father is deceased, the onus falls on you as the claimant or legal heir to initiate this change.
You can then get an affidavit to declare your father's name with surname is one and the same and that you require this affidavit for some specific purpose (you may mention the purpose), get the affidavit notarised, after which you can get it published in local newspaper and then along with the death certificate copy, copy of the affidavit and the copy of the newspaper, you can apply for gazette publication.
Once submitted, the notification will be published in the weekly Gazette. Keep multiple copies of this Gazette notification, as it serves as the primary legal proof for government departments.
Write a formal application addressed to the Head of Department (HoD) or the Administrative/Personnel Officer where your father was employed along with the above said copies.
The administrative department may cross-verify these documents with the original records. Once the HoD approves the request, the administrative section will make the necessary correction in the Service Book and attest it under the signature of a competent officer.