There is not a canonical "D&D" answer. The answer differs per campaign world.
I know it's a little weird - the D&D 3 core books don't present themselves as a generic system per se; they hint at a shared cosmology with the gods, certain roles for the races, etc. that makes it seem like there's a larger world there. But it's just a hollow shell, to be filled in either by yourself or by the specific campaign worlds (Forgotten Realms, Greyhawk, Golarion, etc.).
Now, in 3e/3.5e Greyhawk is the default setting (they didn't follow through on that real well but it was stated) so you could look to the Greyhawk answers as the canonical defaults. I don't know that they ever answered the "but where did they all come from" questions, and I was a Greyhawk aficionado for decades. Canonfire! would be the place to research that. If you're looking for Corellon specifically, try this wiki article. Most campaign worlds are deliberately cagy about how exactly the beginning of all things transpired, however, and Greyhawk is especially so.
Alignment is to a devil what matter is to a creature of the Prime Material.
PHB p. 122
Alignment is an essential part of the nature of celestials and fiends.
A devil does not choose to be lawful evil, and it doesn’t tend toward
lawful evil, but rather it is lawful evil in its essence. If it
somehow ceased to be lawful evil, it would cease to be a devil.
You might want to start your investigation of this question with a quick read on Plato and his philosophy of Ideals. Plato posited that everything we see in this world is just a shadow of a world of "ideals". When we see a dog, we see a lump of flesh attached to some bones and wrapped in fur, more or less like lots of other lumps that we also call "dogs". Plato said that since we can recognize all these peculiar lumps as "dogs", then somewhere there must be an "ideal dog" - a single creature that completely embodies all things doggy.
DMG 57, Outer Planes
When discussing anything to do with deities, the language used must be highly metaphorical. Their actual homes aren't literally places at all, but exemplify the idea that the Outer Planes are realms of thought and spirit. As with the Elemental Planes, one can imagine the perceptible part of the Outer Planes as a border region, while extensive spiritual regions lie beyond ordinary sensory experience.
The DnD multiverse embraces this idea and places these ideals in the Outer Planes. The game no longer has all the summon spells it once did, but when it did, the implied mechanism was that whatever beast was summoned was not any particular beast but the Ideal of that beast. (And, yes, you read that right - the Ideal Dog is not a particular dog, it is all dogs - even those that never existed.)
Of course, to exist on the Prime Material that Ideal had to cloak itself in the stuff of that plane. Those of us made of ordinary earth can not properly perceive or interact with Ideals in their true form. This is why we have the concept of Avatars and why fiends who die on the Prime Material are not truly killed. You can't kill an Ideal through material weapons. If it is possible to truly kill an Ideal, it must be by subverting the very concept that the Ideal represents.
D&D 5e doesn't get very deep into this set of ideas, but there are a few hints here and there. You have stumbled into one of the most direct examples.
The Outer Planes are ideal manifestations of Law, Chaos, Good and Evil. Alignment is the stuff they are made of, as surely as the Prime Material is made of earth, water, air and heat. (DMG p. 59.)
All devils are made of that same material. When a devil visits the Prime Material, he manifests with a material body so he can be compatible with our elements, but this is only a "cloak" over his true nature. If you kill him, you are only rending this "cloak" - you can't touch his true nature with mere material weapons.
If it dies outside of the Nine Hells, a devil disappears in a cloud of
sulfurous smoke or dissolves into a pool of ichor, instantly returning
to its home layer where it reforms at full strength. Devils that die
in the Nine Hells are destroyed forever - a fate that even Asmodeous
fears. (MM p. 67)
Finally, to heart of the question.
If you change a devil's alignment, you are literally changing the stuff of which he is made. Whether his appearance changes is subject to DM's discretion - the books don't say. But in all important ways, he will change into the celestial or fiend appropriate to the new alignment. There is at least one interesting edge case: the Neutral alignment. Perhaps a good follow-up question for this forum would be, "Is there an Ideal manifestation of Neutrality in the Outer Planes?"
Based on deities found in the “3.5e revised edition” of D&D—which is fairly old at this point—I have some suggestions: Ehlonna, Gwaeron Windstrom, Hiatea, Mielikki, and Skerrit are probably your best bets. Hiatea and Skerrit are strongly associated with particular types of creatures (giants and centaurs, respectively), though they’re also the two most strongly associated with hunting. Mielikki is almost too “wild” to be about hunting; her protege Gwaeron Windstrom would be more appropriate. Ehlonna is a good choice too, though it would be quite a perversion of her faith to engage in banditry since her entire faith revolves around taking no more than you need (this “issue” might actually make her perfect for your purposes). Note that Mielikki and Gwaeron Windstrom are specific to the Forgotten Realms,1 while Ehlonna, Hiatea, and Skerrit are part of D&D’s “generic” setting.2
How I found these:
IMarvinTPA is a website with a whole lot of useful searching and filtering tools for D&D 3.5e, including the Find Deity feature. Since it is for 3.5e, which is two editions old at this point, some new deities may be missing, and it may include some old deities that have been either killed off or retconned out. Furthermore, since it searches by the cleric domains that each deity offers, and there is no hunting domain in 3.5e, we have to search for related ideas, and then research each deity separately to see what they’re really about.
Searching for LG, NG, CG, and NG (LN) deities (I have no idea what “NG (LN)” means but I included it and would research more if it came up) that offer one or more of the Animal, Bestial, Endurance, Hunger, Moon, Plant, Thirst, Travel, or Weather domains (I’m really stretching on some of these but false-positives can be weeded out, false-negatives we just miss), we get this list: Arawai, Baervan Wildwanderer, Chauntea, Ehlonna, Eldath, Gwaeron Windstrom, Hathor, Hiatea, Hleid, Ilmater, Kikanuti, Marthammor Duin, Mielikki, Nobanion, Osiris, Shiallia, Skerrit, Solanil, Sovereign Host pantheon, Valarian, and Whale Mother.
Several of these I recognize, but quick web searches on each pulls up details:
Though due to the way the multiverse in D&D works, Mielikki and Gwaeron Windstrom are probably known on other worlds as well, particularly Mielikki.
Ehlonna was originally from Greyhawk, the setting Gary Gygax developed for D&D’s first campaigns, but 3.5e used “Greyhawk but with the serial numbers filed off” as the semi-default setting and Ehlonna has only become bigger and more core since.
The so-called “Outside” supplements are Sandstorm, Frostburn, Stormwrack, Cityscape, and Dungeonscape—also known as “It’s Hot Outside,” “It’s Cold Outside,” “It’s Wet Outside,” “It’s Crowded Outside,” and “It’s Not Outside.”