5e doesn't work that way though. paladins are "divine" casters, but there's no class-bound tie to any kind of diety. the idea is that they use charisma as one of their main stats specifically because their force of character was so strong, almost like their belief in whatever oath they take (the paladin subclass) is what gives them strength, not any specific deity. some oaths lend themselves to certain alignments more than others but there's no reason other than RP to be good or evil or lawful or chaotic. Oath of Vengeance, for example is about hunting and killing something specific (could be someone betrayed you, someone hurt your family, etc) to whatever end. if that means killing everyone and everything in your path than so be it. Oath of Crown is basically like a knight vassal, protecting the people that live on your lord's land.
yes, you can absolutely flavor your paladin to be a champion of Tempus which would put you at odds with the rogue in your group that likes to backstab and kill people in their sleep. but you don't have to anymore. You can be a true neutral monk that respects the lawful teachings of his monestary but is also perfectly happy sowing chaos so he can take advantage of the confusion.
you CAN play where alignment makes a difference... the games i play, alignment comes up in broad strokes. one of my games, i am playing a true neutral tabaxi monk who somehow got a hold of the sword of Kas. he has become a pretty devout follower of Kas. He KNOWS Kas is evil, but he also knows that Kas' goal is to wipe out vecna as well as any other liches along the way. he looks at it as a means to an end. some of the players love to point out "you know Kas is a bad guy right, that makes you a bad guy." and i just say, "no. it makes my character an opportunist."
anyway, point is, 5e (maybe it started with 4e? i didn't really play that edition much other than a couple of one shot games) dropped the emphasis on the alignment that's on your character sheet. alignment is sort of a nebulous thing, and it's something that i've complained about a ton in games that try to quantify it. being evil is a lot more nuanced than just psychotically murdering everyone and being good is a lot more involved than just refusing to take payment for a quest.