The problem is perhaps not with his bio from TNG, but the one the writers would create to make Locarno former Maquis. You couldn't strike out Paris' name and replace it with Locarno because, after a second time, he should be considered untrustworthy after he quit SF for the Maquis. Of course, they could figure out some other way to make him the bad boy who needed a break.
What if you "flip" it? Instead of "Paris is really Locarno," make it "Locarno is really Paris." And, in a way, this makes a lot of sense. Tom Paris has a storied ancestry, not unlike John McCain. But he doesn't want to ride on that legacy at the Academy, so he is enrolled under the name "Nick Locarno," to see if he can make it on his own power. (Perhaps "Locarno" is his mother's maiden name.) Unfortunately, "The First Duty" happens and he's cashiered out. Even his real name wouldn't save him. At this point, once he's out, all he has is his name, so he reverts to using his birth name, Tom Paris. That would make sense of how the two characters can really be one and the same. It's "Locarno" that is the pseudonym.
I have a feeling I'm missing a major point here, but making Chakotay former-Starfleet-turned-Maquis didn't seem to really cause any issues that weren't dealt with on screen. I don't see why Locarno couldn't have just been a crew member on the Val Jean after ****ing up his Starfleet career. That makes a lot more sense to me than Janeway pulling Paris out of prison to serve on her ship.
Oh, I suspect he could do it -- I suspect that he might even be able to win it, if his case was presented correctly -- but of course, an admission that this was their line of thought from The Powers That Be would make it an open-and-shut case. But those in charge at the time continue to maintain their innocence on the matter even today. By continuing to "toe the party line", they muddy the waters enough that virtually nobody can really refute either case. It would come down to a simple claim and counter-claim, and there is probably just as much evidence after seven years of televised adventures for them to say that Tom Paris is a completely different character who just happens to be similar to Nick Locarno, rather than him being Nick Locarno with a different name. It'd be costly to bring a lawsuit on those grounds... but if Rick Berman came out and just *said* that Tom Paris was conceived as Nick Locarno in word and deed, as others suggested he should, then the case would virtually be over. A slam dunk for the writer of 'The First Duty'. I offer no personal opinion. I simply state why Berman might still be keeping schtum about it even after all these years.
Why isn't it enough that the name was changed? That, by definition, makes Paris and Locarno different characters. You can't copyright a character TYPE, only a specific character.
^For the same reason I can't create a character who is identical to Batman and just call him "Flying Rat Man". I'm still getting sued.