It's not just custom . . .
The reason many hospitals may not use the term "Doctor" for those who have a medical education but are not yet licensed is that it may be illegal to do so. In many states one may not use a professional designation subject to state licensure unless one is licensed. In the case of an intern, he has a doctorate but since medical licensure requires an internship that he has yet to complete he isn't legally a doctor.
While some of this may sound silly, it's important as there is no way for the state to verify that every school which grants doctorates is truly legitimate - a quick perusal of the net will bring forth plenty of "doctorates" in various professions, including medicine, which aren't worth the paper they're written on. The state can however control both the testing and experience required for licensure, and the eligibility to take the test in the first place. Thus, once a professional is licensed it can be seen that he's met at least the minimum standards for his license, and the use of a professional designation is a perk of that process.
The reason many hospitals may not use the term "Doctor" for those who have a medical education but are not yet licensed is that it may be illegal to do so. In many states one may not use a professional designation subject to state licensure unless one is licensed. In the case of an intern, he has a doctorate but since medical licensure requires an internship that he has yet to complete he isn't legally a doctor.
While some of this may sound silly, it's important as there is no way for the state to verify that every school which grants doctorates is truly legitimate - a quick perusal of the net will bring forth plenty of "doctorates" in various professions, including medicine, which aren't worth the paper they're written on. The state can however control both the testing and experience required for licensure, and the eligibility to take the test in the first place. Thus, once a professional is licensed it can be seen that he's met at least the minimum standards for his license, and the use of a professional designation is a perk of that process.