Praise be to Allaah.
For the one whom Allaah has guided to Islam, it is sufficient for him to choose an Islamic first name for himself and to keep his father’s name or surname, because the Prophet (peace and blessings of Allaah be upon him) did not command the Sahaabah to change their fathers’ and grandfathers’ names when they embraced Islam. However, he did change the first names of those who had names with forbidden or undesirable meanings. Because your first name has pagan origins, your changing it to another name, such as Bilaal, is proper and correct. But you should keep the rest of your name and surname as it is; this will please your parents. May Allah guide them, and may He give us and you strength. May Allaah bless our Prophet Muhammad.