If the name is an ordinary one according to the culture of the person accepting Islam, there is no need to change it. If the convert is in a marriage which is not acceptable in Islamic law, it is automatically nullified when he accepts Islam. If a man was married to two sisters, on accepting Islam he would have to choose between them. If a Muslim convert's wife remains a Jew or Christian, the marriage remains valid, but if she is of any other religion, the marriage is nullified. Underage children become Muslim once one of the parents accepts Islam.
Adult children are free to choose.
According to Islamic law, a Muslim cannot inherit from a non-Muslim relative in this manner. May Allah guides us on the right way. Shaykh Syed Mutawalli Ad-Darsh. 12 January 1996.