It sounds like you're evolving your Eevee in places other than the Wild Area. As the other answer says, time in places everywhere except the Wild Area is frozen in day if you haven't completed the main story yet. This perpetual daytime also affects evolutions that depend on the time of day (or night), considering the time to always be daytime regardless of the time on your Nintendo Switch clock.
As Bulbapedia explains it:
In Pokémon Sword and Shield, time is set to specific times of day during the main story as a narrative device. This affects all areas of Galar outside of the Wild Area, and even influences evolution. After the player becomes Champion, time is no longer pre-set outside the Wild Area, and functions solely based on the system time...
So, in order to evolve your Eevee into Umbreon, you need to level it up in the Wild Area at nighttime. Once you've become Champion, time in places outside of the Wild Area will function normally.
Note: This answer doesn't add anything new to the previous answer; I only answered to provide a source.