I think he chose "The Doctor" as his name, as was the right of an academy-trained Time Lord (the Master chose his, too). But it's been hinted at that he does have a real name that he chooses to keep hidden. Maybe some day we'll find out what it is.

thanks i just wanted to know it was something that i could not get rigth in my head, i thought it must be something like that because in "The Sound of Drums" the doctor said something about the master choose his name

yes, I thought about that when I heard that line in "The Sound of Drums"... maybe he choose "the doctor" because he likes saving people?? =P

Whats in a name ? The Native Americans chose names dependant upon what they saw in Nature (ie "Two Dogs Humping", some cultures place forename after surname AS WE INTERPRET IT. So an Alien Culture would approximate the nearest translation into our culture for the name they have. Remember the Doctor is unlikely to have English as a native tongue. Then again theres always "John Smith" of course.....

Well if you watch the episode, "The fires of Pompeii" you'l see that a girl, the that could see the future said that his name is hidden, and that it burns in the stars as his planet did. Hope that helped.