Is there any specific reason the doctor chooses the name "John Smith"?

Just a common name for an alias? That's what I always assumed.

'Smith' is the most common last name (I looked it up) and the combination 'John Smith' is very common (guessing).

Well in School Reunion he told Sarah Jane it was a very common name so maybe that's why he uses it o when tu think about it's an easy name to remember so I guess that could be another reason.

Not really, the first time it was used was with the segundo doctor. Jamie chose it because somebody told him that "The Doctor" wasn't a proper name, so he had to make up a name, and John Smith was written on a label o something so he dicho his name was doctor John Smith. Plus John Smith is a really common name so therefore it doesn't raise suspicion when the Doctor uses it, which is why during the third doctor's tenure he used it when he was exiled to earth.