Do the nicknames still work?

go walk 10 km if you dont want to risk

Never heard about the nickname method being removed. The names for Espy and Umbry are Sakura and Tamao, respectively.

Fairly sure that the nicknames will still work if you have not already used them. But I agree if you want Espeon or Umbreon then you can just walk with it to be sure.

The nickname trick still works, it's just that it only works the first time you use it so for example, since I have already gotten a Jolteon by naming it Sparky, I will no longer be guaranteed a Jolteon if I nickname another Eevee "Sparky".