They change their names to honor a predecessor, or to point the direction that they hope their governance will take. Catholics are big on taking new names at important junctures of their spiritual lives — Baptism, Confirmation, Holy Orders, etc.
Since he is Francis I, I suppose that he means to emphasize humility in his leadership. He already is knnown as a man of the people.
My question is why he is designated Francis I? Just plain Francis should be sufficient until there is a Francis II.
I don't know if this is the correct answer, but I'm presuming he's called Francis I in order to let us know that there hasn't been a Pope Francis yet. Everyone would have wondered which number Francis he is, so it's been clarified right from the start.