TL;DR: The names were most likely updated to remove any whimsical tone of the characters.
As others have commented, the names may have been changed to avoid copyright issues with Peter Pan. However, it's important to note that the overall tone of the film changed drastically between re-writes of the script, and the names were probably updated to reflect this.
The original script was intended as a G-rated film in the vein of "Goonies" or "The Monster Squad" - a family-friendly movie inspired by the idea of Peter Pan as a vampire. When Joel Schumacher replaced Richard Donner as director, he reportedly hated that idea and wanted the movie to be more of a sexy, coming-of-age horror film. He brought on writer Jeffrey Boam to heavily modify the script, and it's likely at this point that the names were changed.
Within that context, the changes make sense. The entire film was given a darker, more biblical context (David's body enshrined in light at the end, for example). Rather than a "cutesy" gang of immortal children, Schumacher envisioned the vampires as more akin to the gangs of 1979's "The Warriors". The soundtrack originally called for Madonna songs (whereas Goonies used Cyndi Lauper), and that was obviously updated to more of a heavy metal "hairband" sound. And so forth.
Richard Donner left the project to make seminal action flick "Lethal Weapon", and the resulting version of "The Lost Boys" has become a classic vampire movie. As moviegoers, I'd say we were definitely the winners in this particular instance.
Note: In addition to the facts on that IMDb trivia page you linked to, there are also some additional trivia tidbits on the page below, posted in celebration of the film's 25th anniversary.