To legally give your son from a previous marriage up for adoption by your current husband, you will need to initiate a court proceeding by filing an adoption petition with the relevant family court, which will require your consent as the biological mother, your current husband's consent as the adoptive father, and ideally, the consent of the biological father as well.
Ideally, the biological father should provide written consent for the adoption, but if he cannot be located or is unwilling to consent, legal procedures may be necessary to establish his non-involvement.
If you wish to change the child's surname to your current husband's, this can be requested during the adoption process.