John Gonzalez, who actually wrote the entire main story and many of the game's central characters (Benny, Caesar, Mr. House, Vulpes Inculta, etc.) has seemingly been erased from the collective memory of the gaming community. I think it's really unfortunate. He also wrote all of the Survivalist logs in Honest Hearts (and some of the Happy Trails Caravan).
Writing duties are split up among designers. Not all designers write, but the majority of us do. Some do a larger share than others. I'll miss some here, but notably:
Eric Fenstermaker - Veronica, Boone, a lot of Novac and Helios One (Fantastic), a lot of Camp McCarran (Silas, Curtis, et al.), the White Gloves, Vault 11, some Goodsprings
Travis Stout - Lily, Raul, the Misfits, some Goodsprings, Follows-Chalk, Waking Cloud, some Happy Trails folks, and a bunch of stuff on Old World Blues
Akil Hooper - ED-E, a lot of Primm, the Omertas, some Hoover Dam, some Boomers
Rob Lee - Some Camp McCarran, a lot of Freeside, Camp Guardian, some Boomers
Jeff Husges - Most of Jacobstown, the Remnants, a ton of minor characters all over the place (including Boulder City, many Legion characters and Rex's quest)
Matt MacClean - Return to Sender station rangers
George Ziets - 1st Recon
Charlie Staples - Forlorn Hope, a bunch of other stuff I can't even remember
Jesse Farrell - A lot of Freeside (Kings, especially), Brotherhood of Steel, a lot of Hoover Dam
Chris Avellone - Cass, Lanius, Oliver (I think?) and some minor characters at Mojave Outpost. Of course, he also did all of the writing for Dead Money and Lonesome Road, and split writing duties with Travis Stout on OWB (not sure of the split).
Jorge Salgado - Red Lucy, Sarah Weintraub, Michael Angelo, and a few others (North Vegas)
Other designers also contributed (Stephanie Newland, JR Vosovic, Eric Beaumont, Sydney Wolfram, Dini McMurry), but I don't remember their specific writing contributions.