Pokemon-go – Can an Eevee evolve into Umbreon/Espeon “randomly”

I believe that Eevee's evolutions (outside of the naming trick, which only work once per evolution) are completely random. During my mass evolutions, I have seen cases where I evolve 2-3 consecutive Jolteon then 3-4 consecutive Flareon in the span of a few minutes. Also, I did not move whilst doing these mass evolutions.

Furthermore, I evolved 2 Flareon before I was able to get any other eeveelutions from evolving, but after that, the next 5 evolutions were Vaporeon.

This would disprove the idea that there is some sort of built-in rotation that other answers have suggested.

To answer your question, though, it does not look like location has any sort of bearing on what eeveelution you are most likely to get.

You should restart Pokemon Go after naming it Rainer to make sure the game actually changes the name and registers it, and if so, then evolve your Eevee. If the name change didn't stick, change it again and restart again.

Further to this, if you already evolved a Eevee into a Vaporeon by using the Rainer name, it will not work again, and the Eevee will just change into a random evolution, like Jolteon or Flareon. This goes for all the Eeveelutions as well.

Also check out this link for even more information about the evolutions: I caught an Eevee, which of its evolutions will it evolve into?