The Umbrella Academy's dance scene from episode 1, which was first teased in the TV show's trailers, perfectly sums up each character's hidden personalities while also hinting at season 1's ending. In The Umbrella Academy episode 1, "We Only See Each Other at Weddings and Funerals", the five remaining members of the Umbrella Academy gather for the first time in years, in their old home, after their father, Sir Reginald Hargreeves, had died - though it was later revealed there was a good reason.
Once all of the students had gathered at the Umbrella Academy - barring Number Five (who had disappeared) and Number Six (who's dead) - they each separated into different rooms in the house. Luther had gone to his old bedroom and put on the song "I Think We're Alone Now" by Tiffany. At first, some of the characters resisted the urge to dance, but ultimately, they all started dancing in their own ways - all of them alone in different rooms. After seeing The Umbrella Academy's ending, that dance scene becomes more important (and quite telling).
As pointed out by a Reddit user, each character's dance reveals a part of their personality that they've kept secret. Luther's dance is almost childlike, because he never had the opportunity to be a kid in his childhood since he was always leading the team as Number One. Allison dances with a feather boa and lets her inner-self shine, after having been forced to become reserved in the spotlight as a celebrity. Klaus dances with Sir Reginald's urn, and he holds the urn close to him, because he's always longed for a real relationship with his father.
Diego, on the other hand, strives to maintain a strict persona throughout season 1, but when the music comes on, he closes the door and starts dancing in a wildlike fashion. It's one of the few times he can be himself. As for Vanya, she's hesitant at first but then slowly gets into the groove. She does this, and then dances reservedly, due to being cast aside by the rest of the team throughout her life and has learned to sever herself from others - perhaps as a form of survival.
What's interesting, all of their characters end up expressing these hidden personalities towards the end of The Umbrella Academy season 1, with Klaus, specifically, realizing (a part of) his full potential after speaking with Sir Reginald Hargreeves. Vanya also discovers her true self and unlocks the abilities that her father tried to suppress for years. Furthermore, Diego becomes part of the core of the family after setting aside his mask and allowing himself to care, outwardly, about other people. It was all there, from the very beginning. Even the song in the background highlights the Umbrella Academy students being alone.