Some people call all palms with this type of leaf-fan or windmill palms. Fan would be a better description. There is an actual windmill palm or at least that's the common name. The leaves on a palm tree play a very important role for the tree.rand new leaf of a travelers palm that has just unrolled itself. You can still see the bit of a roll at the bottom. You can also see that the leaf stock has to grow some more to eventually become as tall as the other leaves.