No, the sentence you provided contains a slight error. Here is the corrected version:
"The elements are arranged in a table in order of their atomic numbers, and the electronic structures of the atoms of those elements vary periodically with their positions in the table, so it is named the Periodic Table."
The Periodic Table is named as such because it demonstrates periodic trends in the properties of elements based on their atomic numbers. These trends include the arrangement of electrons in their atomic shells or energy levels, which determine the chemical behavior and properties of the elements.