I'm working on a character concept where a caster class was once a powerful *insert title*, but after loosing a mighty battle had their mind shattered. This resulted in loss of levels and a fragmented mind with multiple personalities. Each long rest a die (d4, d6) is rolled to determine which personality is dominant.

Aside from story and personality I also want this to have mechanical impact, so every personality can exclusively use spells of a particular element. The classical Air, Earth, Fire & Water doesn't really apply, but DND has acid, cold, fire, lightning, poison, thunder. So I could roll a D6 or merge acid&poison and lightning&thunder for a d4.

I'm having trouble determining which caster class best fits this concept. Any and all advise would be helpful.

I've explored Wizard and Druid  because they have the following spell feature "You can change your list of prepared spells when you finish a long rest."
I've also looked at Sorcerer because of the optional metamagic option in Tasha's: "Transmuted Spell"

Following the concept, which class would you go for, and why?

First of all, a word of caution: playing a 'mind-shattered', split-personality character is always fraught.  Be careful executing this, and you may want to do some research on real-life schizophrenia and dissociative identity disorder prior to Committing To The Meme and only discovering after you do that somebody at the table doesn't care in the least for it.  Make sure your table is okay with you trying this idea out, and make sure you approach it with the gravitas it deserves.  It can be a really cool concept to do, but please don't clownshoes it, hm?

Second of all, I would consider druid, primarily because this idea feels like it needs daily spell prep and druids have the widest variety in their magic (yes yes, I know, wizard spell list.  Gimme a sec, going somewhere here).  I'd discard the idea of sticking each persona with a specific element/damage type, and instead consider giving each persona a specific style of casting.  Roll a 1 on the d4 and you get the aggressive, combative, maybe slightly cruel persona who generally prepares straightforward blasting and other destructive spells.  Roll a 2 and you get the cautious, protective persona who primarily prepares healing and defensive magic.  Roll a 3 and you get the sly, snarky, somewhat cowardly trickster who hates fighting and prepares manipulative spells to try and avoid harm.  Roll a 4 and you get the animalistic persona that spends all its time in Wild Shape so it doesn't much care about its spells.  So on and so forth. 

That allows you to make more natural choices with your magic and better utilize your spellcasting while still getting across the idea you're shooting for that none of these personas are complete, and they're all emphasizing different pieces of the complete kit.  Each persona may, grudgingly, prepare a spell or two off their chosen style, but one thing that would help would be ensuring that each persona has a distinctive spell that only they prepare.  Making that spell a core piece of the persona's kit can sell the idea.  Perhaps only the Protector is willing to prepare Cure Wounds; the other personas may grudgingly prep Healing Word or Goodberry, but only the protective personality prepares more than one healing spell, and it's the only one that uses the main healing spell.  Similarly for the others.  That gets to your desired Mechanical Impact without the awkward rigidity of having to know/have spells of multiple disparate damage elements, which no class can really do.

That would be where I'd start, at least.

I was just looking for such information! Thank you

I can only reiterate Yurei's first paragraph. If you're going to do it - please do it carefully and respectfully. Disabilities and mental illnesses aren't to be treated flippantly.

I'd likely go for an effect along the lines of the classic Jekyll & Hyde. I use it for the following:

Background Guild Artisan (Alchemist), Class: Barbarian (path of Zealot although would have gone path of Beast if it was out at time I thought about it originally). The way he enters a rage is to swig a potion which brings out his "hyde" persona. The chharacter is very cerebral when not in combat and uses Hyde as little as possible but knows the more he rages the more grasp Hyde has on him and the harder it is to shift back to Jekyll (represented by the increased number of rages and eventually the persistent rage).

Adapting this to your idea you could start of with a few levels of Barbaian (Wild Magic from Tasha's) and then after a few levels multiclass into Wizard, bard or Sorcerer to represent getting some control back over your personalities.