Not really, saves me a job.
But yeah, what she said. Umbreon has such a massive number of options that it really doesn't have a "best" set. Instead, you must tailor its moves around the rest of your team's needs.
The problem with the set you posted is simply that Umbreon's offensive abilities are awful, which means basic attacks like Faint Attack and Psychic will be extremely ineffective. Toxic is standard but Moonlight is very prone to being neutralized by sandstorm/hail, the former being extremely common nowadays thanks to Tyranitar.
As stated, you need to work Umbreon's moves around everyone else in your team, but Toxic is always a good place to start for any Umbreon set. From there, you can either use a disruption set focusing on stuff like Mean Look and Confuse Ray, or a supportive set using moves like Wish and Heal Bell to heal your team-mates.