I've seen two different versions of why Locarno was changed to Paris.
One version is the copyright thing. It would have cost them a nice sum of money every time Locarno showed up on screen. I'm not sure if that's the truth, I have a feeling that something like that could have been settled in some acceptable way for both parts.
The second verion is that they were planning to use Nick Locarno as one of the main characters in the new series and that actor Robert Duncan McNeill was contracted for the role. But in the last moment, they changed their minds. They found Locarno to be too unsympathetic to become a main character. So they changed the name to Tom Paris and came up with a similar (too similar) background story.
Note also that Locarno is the name of a town in Switzerland while Paris is the name of the French capital!
However, I do think that this thing should be cleared up in the Star Trek Universe. So I have three possible solutions:
Solution 1: Nick Locarno was the result of a a love affair between Admiral Paris and another woman than his wife. The old Admiral helped Nick Locarno to be accepted at Starfleet Academy where he screwed it up. The similar accidents Nick and Tom had were coincidents. Tom's hatred to his father was because he found out about Nick Locarno's existence during his time at Starfleet Academy. A possible meeting between Tom and Nick would be something for coming books or movies, wouldn't it.
Solution 2: Tom Paris and Nick Locarno are the same persons and there was only one accident. Admiral Paris tried to cover it up by persuading all involved to use the name "Nick Locarno" during the trial so that the good name of Paris wouldn't be disgraced. However, Starfleet later gave the Admiral a reprimand for that sceme and the convicted pilot was revealed as Tom Paris. Tom's dislike of his father was further increased by that "Nick Locarno" scenario and the fact that Admiral Paris more and less pretended that the accused wasn't his son.
Solution 3. Tom Paris and Nick Locarno are twins separated at birth. The similarity between the accidents are coincidents, however Admiral Paris did his best to cover up the relationship between Nick Locarno and the Paris family. Tom did find out about it later which is one of the reasons he despises his father.
Voyager's mysteries-and how to solve them:
http://lynx677.110mb.com/Voyagermysteries.html