Umbreon doesn't seem to have much of a sanity, often going insane and crazily talking about what seems like nonsense. He often sees hallucinations and screams as if he is being tortured, a prime example being his multiple claims that "floor tentacles" are drowning him. He, at the same time, claims to "know all and see all," although this is likely not the case. He randomly speaks in Old English at some times, sprinkling words like "thou," "thy," and others for no apparent reason. Superstitions and spiritual shenanigans are a very keen interest of Umbreon's, having spent many all-nighters staring at the moon. According to Jolteon, this is what causes his insanity.
Despite this, he does seem somewhat capable to some degree. His greatest achievement is his large Casino chain, Blackyjack, the largest casino chain in all of Johto. He is noted by Jolteon to be an incredibly competent businessman. He also has a driving license, although it is just a learner's permit. Still, he is one of only 6 Pokemon that can drive. He has also clearly demonstrates safety on the road when he insists on respecting the speed limit when Jolteon wanted a ride to the Pokemon Talk studio. He also seems to be a kind person, apologizing for Jolteon's unwarranted actions towards Vaporeon and even giving him special rights in his casino chain.
The Eeveelution Brothers
Overall, he is close friends with all members of the Eeveelution Brothers, living together with the rest of them (although sometimes he leaves) and supporting them in different ways. They seem to be concerned or tired of Umbreon, Leafeon helping Umbreon with his irrational fear of murderers chasing him. Umbreon is clearly well acquainted with his group.
Squirtle and Bulbasaur
Umbreon is closely acquainted with the talk show hosts, as he used to live in the same place as they did (although without their knowledge or consent) and as he is a reoccurring guest that frequently appears on the two's show, Pokemon Talk. They are weirded out by Umbreon and surprised whenever they hear of his accomplishments, while it is unknown how Umbreon feels about the two himself.