"Osama Bin Laden is a great man. He's a good man for his people, for my culture," the baby's father, Mehmet Cengiz, an unemployed truck driver, told a German television station.
But under German law, it is illegal for babies to be given names that could be offensive or bring ridicule.
Naming a baby Hitler is also banned.
A German court is now reviewing the decision. It has asked the couple to explain why they have chosen the name of the al-Qaeda leader for their boy.
Registration officials in Cologne rejected the name because it would not be allowed in Turkey, said a spokeswoman for the court.
"Another reason was the obvious association of the name with the terror attacks of 11 September," she said.
The spokeswoman declined to comment on whether the couple had other children and what their names were.
Earlier this year a woman in Nigeria fled home with her new-born baby after her husband decided to name their son Osama Bin Laden.
She said she would seek a divorce if he did not change his mind.
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