There are a few things we should clarify beforehand. First, Persepolis is actually the Greek name of the city, not the Persian name. As you can see the word "polis" is Greek, which means city. Hence, Persepolis means Persian city - Perses + polis. The Persian name for the city is Parsa.
As for the origins of the city, construction began under King Darius, who reigned from 522-486. Construction probably started around 518 B.C. Archaeologists cannot be certain. Moreover, the conception of the city might have been under King Cyrus. That said, it is certain that Darius made this city and made it the new capital of the Persian Empire, instead of Pasargadae. However, the city was in a mountainous region, which meant that during part of the year it was very difficult to get to. For this reason, during the winter or rainy seasons, the Persians ruled either from Susa or Ecbatana.