See there can be step parent adoption through CARA after that your wife can be legally mother of your child from first marriage.

For CARA step parent adoption the stable marriage of 2 years is required further more the guildelines and procedure is mentioned in below given link.

http://cara.nic.in/Parents/Eg_step_parents.html

1) you cannot change the mother name of your daughter to your second wife name 

2) there should be giving and taking ceremony 

3) ask your first  wife as biological mother  to execute deed of adoption to give child in adoption to second wife 

Dear Client,

Without adoption deed, not possible. If court has granted you absolute custody and declared you legal guardian and in court order, mother herself has declare seize of any connection with daughter than her consent is not required in adoption deed. 

Yes if the mother is agreed then there is no issue. Being custody is with you, you can do so.

You cannot change biological mother name of your daughter, with the consent of both biological parents your second wife can legally adopt your daughter.

Dear  Sir,

- You shall require the mother consent and further file adoption petition.

- Court has given the custody rights and can not debarred the mother from being your daughter biological mother.

- Advisable to request the mother to execute the adoption deed.

- Connect with local lawyer to help you for step-wise process.

Regards

Vivek Arya

Dear sir,

You have to follow the procedure for adoption for getting mother's name impleaded

See as advised above the name can be updated once the step parent adoption is completed and she your second wife hold legal status of same 

Dear Sir,

Get written NOC from your ex-wife or get the daughter adopted by yourself and your present wife by getting adoption deed from ex-wife.  The biological mother may make issue if you put the name of your present wife as mother of the child without the consent of your ex wife.

1) Your new wife has to obtain adoption procedure towards your daughter. Means she can adopt the girl child as per Hindu Adoptions and Maintenance Act, 1956

1. As per the information mentioned in the presnet query, makes it clear that you are married now, and wish to change the name of the mother of your daughter on every documents of her.
2. For that your presnet wife would have to adopt your daughter legally after filing an application before the civil court of law with all the necessary documents like marriage certificate etc.
3. Generaly, there has been a concept of getting the NOC from the biological mother, but as it has specifically mentioned in the court order about your 100 percent right over your doughter, you would not be needed that.
4. Once you get the court order of legally adoption by your present wife then you can get everything ( mother’s name specifically) changed on her documents.

Rest, you can contact me for availing my services if like my answer, I would love to proceed as per legal procedure on your behalf before the civil court of law.

Daughter's mother name cannot be replaced from her biological mother's name to the step mother's name.

Since there is no question of adoption of your daughter by your second wife, there is no provision in law for change of mother's name in any records without a registered  adoption deed.

The relationship between a mother and the child cannot be divorced nor it can be legally disowned. It is a natural relationship.

Since there is no provision in law for any such change as desired by you, you cannot do anything about it.