Incorrect mother's name

better to change by legal manner for which better to seek local lawyer help and act accordingly

Since your mother is stated to have been died, it is not possible to change her name at this stage.

Submit record of her name(s) with an affidavit to the insurance company for settlement of the policy. However, if the insurer do not agree file a suit for declaration that XYZ and  PQR are the two names of same person.

Consult and engage a local prudent lawyer for necessary proceeding.

Normally, in all legal documents the sequence of a person's identification is as follows:

Person's Name:

Son of   (Name of the Father)

A resident of (brief address)

Aged about (age)

The mother's name is normally not mentioned in any of the legal documents except in the Passport application and Passport.

In what way Mother'sname is being mentioned and in which legal documents your Mother's name is mentioned.

I have yet to come across a single instance wherein the co-sharer was refused share from other co-sharers only because there is a change in the mother's name.  When there is no change in the relationship and admitted that he is the son of a so and so lady.  Because there is a difference in the mother's name, it is not going to be an issue at all. A simple affidavit duly drafted by a professional is sufficient to overcome the hurdle. if any. (At some places, there s a tradition of one name with parents and the name will be changed by in-laws after marriage)

Declaration order is to be required from the court. Minor errors in spelling in name of Insured can be corrected by applying for the same to the Insurer with certified copy of your ID proof. The Insurer will issue an endorsement to the policy which can be attached to the policy.

Hello, Greetings of the day!
For the query you posted, 
Submit the record of your mother’s name with an affidavit to the insurance company for a settlement claim of the policy. However, if the insurer denies giving a claim, then file a suit for declaration that XYZ and PQR are the two names of the same person who is your mother and it may also include a formal declaration to avoid future proceedings. 
An Affidavit of One and the Same Person is a written document that establishes that two different names found at different documents refer to the same person only. An affidavit is executed in order to establish that both documents, despite bearing a distinction in name, refer to the same person.
For proper guidance consult a local prudent lawyer.
Hope it helps
Regards,
Sneha Jaiswal
Law Student

Since your mother is alive you arrange for change of name of your mother as per legal procedures.

An affidavit stating both the names are one and the same and that she is known by both the names, to be prepared  and get it notarised, and then get this affidavit published in two local newspaper, one in English and another in vernacular language.

Keep all these documents along with her other documents/certificates, the copies of the same may be produced in case of any problem that may arise due to the difference in name.

The  Insurance policy has to be paid as per 'Nomination" where the identity of the Nominee with such AADHAR/ID proof is sufficient.  The Nomination form may also confirm the relationship also.  The policy holder's misspelling etc hardly matters when the ID of the Nominee has to be only considered.  Whatever extra documents and silly objections are only to delay the payment.

"I am facing challenges in insurance claims in the name of my mother," How? Please furnish complete facts?

"also in property will I get my share as my mother is my only parent." What is the source or basis for your apprehension?

"My father expired 2 years back" - How this information is relevant?