Unlike his siblings, on Netflix’s The Umbrella Academy, Five is only mentioned by his number. His lack of a real name is indicative of his personality and his profession as an assassin.
When Reginald Hargreeves adopted each member of The Umbrella Academy, he worked with each of them to hone their powers. Five was too eager to flex his skills.
Due to his impatience, he jumped into an apocalyptic future and was accidentally trapped there for decades. Since he was essentially single for years, he was left with the only name he ever knew at The Umbrella Academy.
While none of the Hargreeves brothers had an easy life, Five had the most unusual of all. When he jumped into the apocalyptic future in season 1 of The Umbrella Academy, The Commission picked him up.
The organization makes him a methodical and heartless killer. Five never understood what it was like to have a life of his own, as he had to fight every day just to stay alive at The Umbrella Academy.
His lack of a real name only highlights his lack of humanity. Gallagher, an actor at The Umbrella Academy, even says his understanding is that Five rejected the idea of a new name, since things like names are trivial for Five.