Some possible explanations to that can be found on the page "Voyager Mysteries and how to solve them" at:
http://lynx677.110mb.com/Voyagermysteries.html
Otherwise there arre two explanations. One explanation is that if they had used the name Nick Locarno, they would have to pay a nice sum of money to the one who came up with the character Nick Locarno in "The First Duty" everytime Locarno did show up in a Voyager episode. However, I do think that it could have been solved in some way.
The other, more realistic explanation is that they were actually going for the option of Nick Locarno as one of the Voyager crew members but after a while they realized that the character, as he was presented in "The First Duty" was too unsympathetic and his crime too severe to become a main character n the series. So they rewrote his background story slightly and named him Tom Paris instead to make the character more acceptable and likeable.
Personally I think that they should have come up with a more different background story for Paris. The accident thing was too cloes to the Locarno story. They should have settled with him only joining the Maquis, thus disgracing his father and Starfleet or whatever.