The simplest answer is that as they represent different aspects of Bob Dylan, and that a few of them intersect with each other's storylines (Heath Ledger is an actor playing the Christian Bale character) so they must have different names to help us accept that as a reality. Keep in mind, though, that a few have only 'surrogate' names-the young boy says he's "Woody Guthrie" which is clearly not his real name. Arthur Rimbaud was 19th century poet, and therefore the name is used to echo the real Rimbaud, while being Dylan being Rimbaud.
The much more complex answer is that none of the people are Dylan, or, in a poetic sense, even people. The Richard Gere character, who is called 'Billy the Kid' is really less of a person and more of a kind of 'free-floating myth'-Billy the Kid was a mythological character. when he died, the myth that was attached to him was freed, and floated without any connection for a long time. It become politicized, by seeing oppression, and then re-attached itself to Dylan. Dylan, who was too young to understand it, is a 'child' to the myth. He grows to understand it, and becomes an 'adult'-these are separate characters in the film. The Arthur Rimbaud character does not have a storyline, a narrative, but delivers testimony to a jury. It's hard to see him as a character, like the others.
Of course, when you watch the film, you'll see how complex this is-the young boy hops trains and lives with hobos-poor folks, the poorest. He is 'saved' by middle-class white folks, who treat him as a curiosity, but don't pay much attention to his radical political ideas. As an adult, as Cate Blanchett, Christian Bale, or Heath Ledger, he struggles with this 'split'-how can he sing songs about poor folks to middle-class folks who don't understand what it means to be so underprivileged? Each of them struggles with the split differently-through anger, opposition, sadness. It is through their different names that we as an audience read each person as unique, not just as people, but in how we relate to them, how we understand them. Obviously we treat a character in a documentary (like the Christian Bale character) differently than a character in a soap opera (like Heath Ledger) or a person in a non-narrative experimental film (like the Ben Wishaw character).
So, in short, they are given different names because they are not really equally 'people' or 'characters.'
As a final note, think about the 'Seventh Dylan'-Kris Kristofferson's voice-over narrator, who calls himself "I" when he talks. He has no name, that he gives us, but clearly offers yet another point of view on Dylan.