This could be interesting. I have lots of alts with their own story, but I love them all. As time passed, their names became closer to the naming conventions so here I come.
First, the Guardians of Light's side.
Faith Sol'une (X'wyhn Lehn) [WHM]
Faith, the Warrior of Light is my main character, a Seeker of the Sun Miqo'te. She was the first character I made, and then I did not know about naming conventions. She was made to resemble my favorite Final Fantasy character, Hope Estheim (FFXIII), so since she was female I gave her the name "Faith", and as for Sol'une it is a corruption for "sun" and "moon" in Latin.
Later I decided to give Faith a backstory, so I gave her her birth name, X'wyhn Lehn. She is from the Lynx tribe mainly because lynxes are my second favorite animal. She was born in Meracydia, in a coastal village named Sol'une that was decimated by a plague with only her, the future Warrior of Light, as a survivor. She was adopted by an Elezen family that lived in an island south of Sharlayan, and they gave her the name "Faith". She is technically Faith Girbois, since she is formally part of the family, but she took the name of her birthplace as an adventurer.
Yansa Ru'shi [NIN]
Yansa is my Xaela Auri ninja, and as for her she is not entirely true to the naming conventions but she has backstory. Yansa is the name of the Yoruba goddess of sorcery and wife to Shango, god of thunder and war. As for Ru'shi, it is the romanization for l'Cie, a term of FFXIII and Type-0. Basically, the Ru'shi tribe is a relatively recent one that lives in seclusion in the Fanged Crescent and pursues intelectual enlightment, and they are made of outcasts from other Xaela tribes but only children born amidst the tribe earn the right to have the surname Ru'shi.
Leona Wyznloef (Wyznloef "Leona" Alyrsthalwyn) [BRD]
Leona is a Hellsguard Roegadyn, and her "surname" is actually her name. She is from Thavnair, so she does not follow your usual Hellsguard naming convention, even though they are just basically the translated names of Sea Wolves. She is a renowned bard and mercenary and she is usually referred to as "Wyznloef the Lioness" or simply "Leona Wyznloef", so she basically ran with it. Wyznloef means "white leaf".
Lyanne Blanchateau [RDM]
Lyanne is a Duskwight Elezen hailing from the Cieldalaes, yet her father Feliciaint was a native of the Black Shroud with Gelmorran ancestry. Lyanne is a name I simply liked, and Blanchateau, well, is a bit of an inside thing of the FFXIII trilogy.
Samra & Mikhel (Rhyu'a) Shir'valah [SAM/BLM]
The Shir'valah siblings! They are Keeper of the Moon Miqo'te. Samra is the older sister, whose name means "ruler" in I-do-not-remember-which-language, and Mikhel's uncommon name comes from their adoptive parents, who named him after his late father, Mikh'to Zhwan, though of course his birth name is Rhyu'a, since their mother was Rhyu Shir'valah. Shir'valah is a made-up Keeper of the Moon surname, and it is based on a now deleted ability of World of Warcraft druids that would allow them to become a half-panther humanoid, and it was called the "Claws of Shirvallah".
Ryuzan Kyouko [PLD]
A Raen Auri paladin from Hingashi, Ryuzan's name is kinda Japanese sounding, and of course it has the "ryu" part that means "dragon". As for his surname, Kyouko, I do not know how old it sounds, but still, it is the first name of one of the main characters of Danganronpa, Kyo(u)ko Kirigiri.
Joana (bas) Strome [MNK]
Yes, she is a Highlander Hyur monk with a Garlean naming convention. Her Ala Mhigan family fleed from the Garlean invasion into Ilsabard, and then they settled there and became acknowledged citizens of the Empire. Joana is a fairly straightforward name, as for Strome, it is like an old-English like spelling of "storm", which I felt appropriate for a monk.
And now for the Guardians of Shadow's side!
Nagi Uranai [AST]
The Warrior of Shadow, a Raen Auri astrologian who was born in Sui-no-Sato and abandoned by her parents in the Azim Steppe because they thought her shadow powers and dark skin in a Raen were a bad omen. She was found by the Iriq and adopted by their khan. In Japanese, "nagi" ナギ is a word for a lull in a storm, and "uranai" means prediction/divination.
Khaara Iriq [MCH]
Nagi's adoptive sister, a Xaela Auri machinist, who bodyguards and protects her wherever she goes. She, of course, is of the Iriq tribe, and her name, though corrupted, comes from "kara", which in Irish means "friend" or "love".
Victoriel Matiere [WHM?]
A Wildwood Elezen and descendant of heretics, Victoriel is a healer but still has not found his true calling and potential. His name (and all of his family's) is based on a French artist/writer I like; in his case, it is Victor Hugo. Matiere is the name of a character in Pokémon X/Y, but overall it is a rather common French name/surname.
Dhemswys Swarnahctwyn [DRG]
Of course, Dhemswys, or Dhemie for short, is a Sea Wolf Roegadyn. She comes from the islands in the North and is part of the Shadow Hunters, though she went to Ishgard to train further in the lance and ended up being the first Roegadyn that was accepted as a dragoon. Dhemswys means "dusk sister" (her older sister is Trachswys, "dragon sister") and her father's name Swarnahct means "black night".
L'nhei Mhaat & L'zhai Tia [WAR/SMN]
And these are the Seeker of the Sun Miqo'te twins! Treasure hunters and last members of a fraction of the L tribe that settled in the Dalmasca Desert. Since they are twins, their names are meant to sound similar, though their father's name, L'mhaat, comes from the Ancient Egyptian term of "maat", which was both the word and the goddess of justice. Oh!, and they are from the L tribe, which is, the Vipers. That is because my favorite animal are snakes.
Aina Roig i Valls (Aina Roig) [DRK]
A Midlander Hyur that hails from a particularly isolated village in the New World that has its own naming conventions and customs. Actually, all their names are common Valencian (a dialect of Catalan) names. Aina is the Valencian spelling of "Anna", and her surnames Roig and Valls mean respectively "red" and "valleys".
Yrere Yre [SCH]
And finally, the Plainsfolk Lalafell scholar, Yrere Yre, hailing from Sharlayan but student at the Magitek Academy in Garlemald. Names are rather limited if you want to stick close to the Lalafell naming conventions, but I found Yrere's name pretty endearing.
So there they are. All sixteen for now. When new jobs come out, more characters shall join. And I will be able to give poor Victoriel a proper job instead of being a WHM just like my main.