There is no specific name for a leg doctor. There may be certain doctors who specialize in leg problems, however there is no specific title granted to them. The type of problem with a person's leg would dictate which type of doctor he would see.
The closest thing to a "leg doctor" could be a podiatrist, whose main area of focus is the foot and ankle, not the entire leg. A person's specific ailment or issue will determine who he seeks out for treatment.
Some leg problems may be handled by the family physician. If a person has a fracture in the leg, he can see an orthopedic, who specializes in problems and injuries of the musculoskeletal system. If a person is experiencing arthritis or joint problems in the lower extremities, he can see a rheumatologist, who specializes in treating such issues.