Is it obligatory to inform the husband that his wife is the daughter of adultery and bears the name of her mother's husband, and is she required to change her name?

There is no obligation to inform the husband or anyone else about what happened. It is better to conceal oneself and one's mother. The questioner is not sinful for what her parents committed. However, it is not permissible to claim lineage to the stepfather, due to the Prophet's (peace and blessings be upon him) saying: "Whoever claims lineage to other than his father, or affiliates himself with other than his masters, then upon him is the curse of Allah, the angels, and all mankind. Allah will not accept from him on the Day of Resurrection any obligatory or voluntary act of worship," and "Whoever claims lineage to a man knowing that he is not his father, then Paradise is forbidden for him." Therefore, the lineage to the stepfather must be changed to an appropriate name, such as "so-and-so bint Abdullah or bint Abdur-Rahman."