1. Your daughter can continue the way she is mentioning her biological father's name,
2. The same can be done by your 2nd husband's children also,
3. It names of father's and mother's name of the children can not change automatically,
4. It is neither mandatory nor necessary, if you do not wish, to enter into an adoption deed,
5. The children will inherit the properties of their individual biological or adoptive parents,
6. No the right on the properties of biological deceased father of his daughter never extinguishes.