Can you provide something that says raising undead is an evil act in 5e? I've got a culture where you will your body to your family, church, liege, or whatever on death to act as a everliving servitor. I had not seen anything in the rules that it was inherently evil in 5e.
I thought I had seen that stated in 5E, but after digging through the rulebooks, I have not found it; neither the text of the
animate dead spell, nor
create undead, nor the Necromancy tradition, nor the monster descriptions for skeletons and zombies, say anything about it being an evil act to raise undead. Maybe it was in the D&D Next playtest and got removed before release? Anyway, I guess that's another relic of previous editions to consign to the mental dustbin. Good deal.
That said, skeletons and zombies
themselves are evil, driven by a hunger to kill the living; that's stated explicitly in the Monster Manual. Those who raise such minions are wielding dangerous weapons. If the necromancer dies or is prevented from renewing their control, the undead become free-willed and they will slaughter any living person they see. So, while it may not be a simple as "Necromancy evil!", a good-aligned necromancer should refrain from raising undead when not necessary, and should take precautions to keep them from getting loose.
To the OP: I would talk with the would-be paladin player and work out a way for the two PCs to coexist, keeping in mind that it's mainly on him to adapt his concept to the existing group--you should not have to retool your PC for his sake. Many paladin oaths are perfectly compatible with necromancy; the Oath of Vengeance, for example, is generally fine with using weapons of darkness against darkness. But even a more traditional knight-in-shining-armor paladin could be okay as long as the player doesn't act like the Alignment Police. Periodic debates between the paladin and the necromancer can be fun to roleplay if the conflict doesn't escalate to actual combat.