Adze handles are most often made of hickory. Hickory is a strong, hard wood that can absorb the shock of impact without splitting or cracking due to its straight grain.
Other flexible woods, such as ash or cherry, can be used for adze handles. They are less durable, however, and will not last as long.
Some adzes have fibreglass handles. These are also capable of absorbing shocks from impact. They are strong and lightweight. but not as easy to find as wooden handles.