Name changes in Birth Certificate and in Aadhar Card

I Divorced with my Husband and remarried to another, I also have custody of my child having 6 year. I firstly married to Delhi and I also from Delhi , but now I married to Himachal Pradesh. Court marriage done in second case in Himachal and also in affidavit of Marriage my husband undertaken my child for adoption. But I want to concern that is their any need to prepare proper adoption deed to take my Current Husband to adopt my child while child is in my custody. 1. Is my husband needed proper adoption deed to adopt my child with me. 2. Where this deed need to be created in Delhi or in Himachal. 3. Is my Old husband Consent (what type of consent is required) 3.1 Present on front of judge 3.2 Or only NOC document is enough. 4. Where this Work will Happen in Court or in SDM office . 5. And after this Work what is procedure to update new husband name in birth Certificate (created in Delhi) and in Aadhar Card. Or this document is sufficient to update name in all places. Pls Suggest