What is the significance of changing one's name for a new Muslim, and what is the difference between an Arabic name and an Islamic name?

A new Muslim is not required to change his non-Arabic name unless it signifies servitude to other than Allah, such as "Abd al-Masih" (servant of the Messiah) or similar, in which case it must be changed. As for common names like "George" and "Paul," there is no obligation to change them, although it is recommended to improve the name to an Islamic one.