the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
This depends on the customs in the country. The important thing is that the child is properly attributed to his father. However this is achieved in the culture in which you live, then this is the method that should be followed. The child's parentage should be clear from the name. The name should not cause any confusion about this matter.
In many countries the child has his given name, then his father’s name, then his grandfather’s name, then his family name. In other countries the grandfather’s name is omitted from the formal records. What is important is that the child is duly attributed to his father according to custom.
Source: Islam Today