Yes but the biological mother should not any objections to it

Biological mother has to execute deed of adoption in favour of adoptive mother 

then only her name can be added as mother in passport 

Step mother's name cannot be added to the passport of your daughter until and unless she has legally adopted your child. 

You can have her name added to your passport as your new spouse by getting the name of old spouse deleted. 

The name of the mother in the passport means that of your daughter's biological mother. Her step-mother's name cannot be added under that column. 

Biological mother consent is mandatory 

Adoption Procedure for Step Parents

1. The couple (step-parent and one of the biological parents) shall register in Child Adoption Resource Information and Guidance System with the required documents as mentioned in Schedule VI.
2. Consent of the biological parent(s) and the step-parent adopting the child or children shall be as provided in the Schedule XX (refer instructions in Schedule XX).
3. The biological parent and the step-parent shall file an application in the Family Court or District Court or City Civil Court as the case may be, as per format given at Schedule XXXII.
4. The applicants shall obtain a certified copy of the adoption order from the court concerned and furnish a copy of the same online to the Authority through Child Adoption Resource Information and Guidance System.
5. The biological parent and the step-parent, who intend to adopt the child or children of the biological parent, shall file the adoption application as provided in Schedule XXXII, in the court concerned of the district where they reside, along with consent letter of the biological parents and the step-parent adopting the child or children, as provided in the Schedule XX and all other documents as provided in Schedule VI.
6. The prospective adoptive parents shall file an application in Family Court or District Court or City Civil Court, as the case may be.
7. Before issuing an adoption order, the court shall satisfy itself of the various conditions stipulated under section 61 of the Act, and regulations 51 to 56, as the case may be.

You need to get it done as per CARA rules in India. 

Dear client, 

You need the biological mother's consent even if she has no visitation rights.

Thank you

There is absolutely no need legally for your daughter to be adopted by your new wife. Let your ex-wife's name stand in the passport as your daughter's biological mother. As you would have all the documentary evidence to show your divorce and remarriage, your daughter will not face any issues.

1. Your earlier wife is the biological mother of your daughter whose custody you are holding.

2. You shall have to take her written consent for taking your daughter out of the Country.

1.Since she is not interested in her daughter through you, it may not be very difficult for you to obtain her written consent to take your daughter abroad along with you. 

2. No adoption deed of a child can be legally executed/registered without the written consent of his/her biological parents.

- If your current  marriage is registered and the divorce decree mentioned the custody of the child perfectly , then after producing the copy of the same , mothers name can be changed in the passport. 

- Further, if the daughter is going to apply for passport first time /fresh , then you can change the name of her new mother name  in her birth certificate and other related documents and after producing the same it can be mentioned in the passport as well. 

- As per Punjab and Haryana High court , the name of mother in passport may be changed any time.