Without a doubt, the most popular (indeed, oversaturated) fire-themed name in the Anglophone world currently is Aidan and its 101 kreatyv spylyngz. It comes from the old Irish name Áedán, a diminutive of Áed (a name which later evolved into Aodh, pronounced AY or EE). However, there are a number of other fire-themed names one might consider.
Azar means “fire” in Persian.
Keahi means “the fire” in Hawaiian.
Agni means “fire” in Sanskrit, after the Hindu god of fire.
Aldebrand means “old fire” or “old sword” in Ancient Germanic.
Aldobrandido is a Medieval Italian form of Aldebrand.
Aliprand means “other/foreign fire” or “other/foreign sword” in Ancient Germanic.
Cináed means “born of fire” in Gaelic.
Conleth is a modern Irish form of Conláed, which possibly means “chaste fire.”
Fintan means “white fire” or “white bull” in Irish.
Ignatius is a Latin name derived from the family name Egnatius, which was a Etruscan name of unknown origin. The spelling was changed to resemble the Latin word ignis, “fire” (whose striking similarity to the Sanskrit agni reminds us how much more similar Sanskrit is to the European side of the Indo–European language family than we often assume).
Other forms of the name include Ignace (French), Ignatz (German), Ignatiy (Russian), Iñaki (Basque), Ignasi (Catalan), Ignaas (Dutch), Ignác (Hungarian and Czech), Ignazio (Italian), Ignacy (Polish), Ignas (Lithuanian), Inácio (Portuguese), Ignacio (Spanish), and Ignas/Ignacij (Slovenian).
Ognyan means “fiery” in Bulgarian.
Plamen means “fire, flame” in Serbian and Bulgarian. I have a secondary character by this name.
Pyrrhus is the Latinized form of the Greek Pyrros, which means “flame-colored, red.” Another form of the name is Pyrrhos.
Yoash means “fire of God” or “God has given” in Hebrew.
Fajra means “fiery” in Esperanto.
Fiammetta means “little flame” in Italian. This is the name of one of the seven women in the brigata of The Decameron.
Hestia means “fireside, hearth” in Greek, after the goddess of the hearth and domestic activity.
Ignatia is the feminine form of Ignatius. Other forms are Ignacia (Spanish) and Ignacja (Polish).
Nina means “fire” in Quechua, an indigenous language mostly spoken in the Andes Mountains of South America. This isn’t to be confused with the European and Georgian name Nina, which has a completely different etymology and history.
Seraphina is an English, German, and Latin name meaning “fiery ones,” in reference to the Seraphim angels. Other forms include Serafina (Italian, Polish, Spanish, Portuguese, and Hebrew), Serafima (Russian and Macedonian), and Séraphine (French).
Shula means “flame” in Arabic. The Turkish form is Şule.
Ugnė means “fire” in Lithuanian.