Ah yes the chapter of names in which I ranted about in the foreword here we go
DISTRICT 1
These are some good ones to go with, but when in doubt just go with anything luxurious sounding considering the District 1 industry is luxury items. If you're naming your character something overused like Diamond or Silk, it's best to have them make a point of being exasperated about having such a common name. Also, in a district so concerned with class, names like this might be considered popular names for low class parents to pick for their child in an effort to sound more high class, and so people might look down on them, although classism is bullshit. It also helps to make characters with common names a little more angsty since they often feel like they don't stand out and don't matter, although this is completely optional and certainly a character with a unique name can be the same way. These tips are applicable for overused names in any district, though.
Marble, Diamond, Twinkle, Lush, Shine, Glisten, Sapphire, Platinum, Glitter, Gold, Silver, Gleam, Brilliance, Radiance, Valor, Lace, Monarch, Crystal, Royal, Amethyst, Gem, Silk, Rose, Selenite/Selene (Selene was a moon goddess and can possibly mean brightness so this could be especially good depending on the character's personality, and Selenite is a crystal. It's very healing and very very pretty and definitely looks moon related. I'm obsessed with selenite but seriously do a google images search for it, it's super beautiful), Pyrite, Aria, Allegro, Capella, Soleil, Apollo, Legacy, Glory, Velvet, Sash
DISTRICT 2
For District 2, whose industry is stonemasonry and peacekeepers, the names here are going to be strong and victorious sounding, but names that actually go with people's jobs will be common too, which is why crystal and stone names are good here too.
Astrid, Frederick, Leo, Ares, Crimson, Grim, Maia, Slate, Alexander, Scarlett, Lewis, Granite, Amazon, Macbeth (last name), Mercutio, Aventurine, Fluorite, Tourmaline, Malachite, Citrine, Hematite, Halite (Halite is a salt crystal so if your tribute is sarcastic as hell, angsty as hell or just likes to have a go at people it'd be actually pretty funny and very fitting to have Halite in their name since they're salty [finger guns]), Trilobite, Obsidian, Amber, Jett, Apollo, Stone, Legacy, Glory, Jade, Val
DISTRICT 3
District 3 's industry is technology, so anything tech related or intelligent sounding works here. These names can work in District 5, and their names can work in District 3.
Franklin, Silicon, Radar, Albert, Digit, Fuse, Edward, Gear, Janet, Magnet, Electra, Gage, Watson, Vania, Helix, Alastair, Wire, Volt, Spark, Mercury, Titanium, Chrome
DISTRICT 4
District 4 specializes in fishing, so anything water related works. However, these are also Career tributes, so keep that in mind.
Teal, Reef, Ariella, Krill, Dungeness, Shore, Dylan, Coral, Dory, Marlin, Morrissey, Kendall, Azure, Lorraine, Rhode, Winnifred, Caspar, Delta, Glade, Misty, Wade, Daria, Clara, Caspian, Jack, Cod, Albacore, Mackerel, Herring, Trout, Betta, Tetra, Haddock, Ray, Terra, Pristella, Abalone, Riptide, Wave, Genevieve, Ethys, Conch, Cowry, Scallop, Marina, Muriel, Kai, Mara
DISTRICT 5
District 5 supplies the Capitol with power, so many of the names from this district are good for District 3, and vice versa.
Radar, Digit, Flash, Fuse, Watson, Isaac, Volt, Electra, Spark, Atom
DISTRICT 6
Transportation is the focus of District 6, so names that reflect that are best. Bonus points if the name has something to do with speed. Names of birds are also good here since they fly.
Indigo, Wren, Canaveral, Bentley, Track, Gear, Acura, Bugatti, Raven, Maserati, Vanellope, Robin, Hawk, Phoenix, Sparrow, Crow, Falcon, Eagle, Korbyn, Griffin, Sarika, Deryn, Circe, Skye/Skyler, Adaryn, Lark, Morrigan, Maia
DISTRICT 7
The District 7 industry is lumber and paper, so the names are going to be very nature-inspired here, especially names of trees, but other plants work as well. These names can often be interchanged with District 11, and vice versa.
Vine, Thorn, Wisteria, Ivy, Azalea, Fir, Poppy, Peony, Acacia, Laurel, Daphne, Iris, Skye, Clementine, Violet, Willow, Fern, Grover, Aspen, Juniper, Birch, Cedar, Pine, Ebony, Elm, Manzanita, Spruce, Sylvia/Sylvester (both mean forest), Linden, Sequoia, Rowan, Redwood, Alder, Maple, Timber
DISTRICT 8
Names for District 8 tributes will reflect their home's industry, textiles, so fabrics, colors and patterns make very good names.
Chiffon, Chambray, Flannel, Hessian, Thread, Kemp, Velvet, Sash, Indigo, Chartreuse, Fray, Brocade, Ty, Calico, Cambric, Damask, Jersey, Madras, Moiree, Tencel, Tailor
DISTRICT 9
Since District 9 's industry is grain, some District 11 names can work here, but names directly related to grain work best.
Miller, Whitney, Ceres, Milo, Merona, Demeter, Mazy (like Mazie but just an uncommon spelling), Rye (very very overused), Lentil, Millet, Apollo, Persephone, Spelt, Amaranth, Poppy
DISTRICT 10
Hailing from the livestock producers, tributes whose hometown is District 10 often have rancher-type names, such as products they provide for the Capitol.
Whitney, Suede, Beth, Hereford, Duke, Sampson, Minnie, Daisy, Merona, Dallon (yes like Dallon Weekes), Sable, Steed, Noxx, Dust, Stallion, Brown, Toro
DISTRICT 11
District 11 tributes will most often have natural names, especially plants, and if not a natural name, at least on pertaining to agriculture since it is pretty much what they eat, sleep, and breathe. However since District 11 families are almost always dirt poor, they won't have much, and so will hang on to nonmaterial things, and you can show this by naming your characters after virtues. District 7 names work here, and sometimes District 9 names. Tributes from both here (and the other poor districts but DEFINITELY 11 and 12) will not have elaborate fancy names like Sir Pompilius Alighieri III or Madame Laurentina Floof. Theirs will be simple and down to earth (no pun intended, but now that I realized it, it's intended. [finger guns])
Wisteria, Ivy, Poppy, Renata, Peony, Iris, Faith, Thorn, Vine, Skye, Clementine, Violet, Fern, Valley, Pilár (was almost my name, means petunia in Spanish) , Autumn (my name), Truth, Trinity, Apple, Lavender, Blossom, Rosa, Esperanza (my soon to be middle name, means hope in Spanish), Sage, Thorn, Carnation, Mandrake, Anise, Primavera, Breeze, Verano, Thyme, Bloom, Hope (my current middle name), Daffodil, Blue, Lily, Basil, Lilac, Rosemary, Verbena, Daisy, Thistle, Marigold, Nettle, Cumin, Jasmine, Winter, Chamomile, Matcha, Neferteri, Summer, Aubergine, Star
DISTRICT 12
District 12 names, surprisingly enough, aren't often ones relating to the coal mining industry, rather, they're more often natural names like ones used in Districts 7 and 11. However, any 'hippy name' can work whether or not it's a plant. Here are some ideas that reflect both this and names to do with the district trade.
River, Flame, Jasper, Colton, Ash, Grey, Granite, Auburn, Stone, Ember, Blaze, Trilobite, Obsidian, Amber
THE CAPITOL
Capitol names are almost always Greek or Roman, if all else fails choose something luxurious sounding.
Maximus, Antonius, Decimus, Herminius, Laurentina, Marcella, Pompilius, Chartreuse, Marcus, Alighieri, Etienne, Lampetia, Julius, Achillios, Evangeline, Alethia, Adonis, Crixus, Crassus, Alastair, Constantine
ALL DISTRICTS
Juno, Kira, Sianna, Whisper, Delphine, Ruhe (good last name for a shy character) Reyler, Halo, Viridian, Taran, Sereno, Petra, Arwen, Amaya, Cian, Medrano, Jhai, Cherno, Ravana, Mara (especially good for D4 but good for any since in Spanish mar = sea), Lolita, Desdemona, Blake, Salem, Videl, Aislinn, Hesper, Dierdre (if you're writing a character with depression or who experiences a lot of emotional pain this is a good choice considering dierdre roughly means sadness), Mallory, Delora, Cessair, Aria, Helena, Ivory, Mareina, Alanna, Lillith, Absinthe, Noir, Asphodel, Anastasia
Hopefully these ideas for more Panem-y names will help you create characters that better fit the Hunger Games world, and less and less Jessicas and Liams will pop up, ditched for more accurate names. Happy Hunger Games, and may the odds be ever in your favor!