When Oliver Twist is born at the workhouse, it is time for the O's in the naming of newborns, so "Oliver" is chosen by Mr. Bumble, the beadle, who is responsible for the naming of the children in the poorhouse. But "Twist" is something that Bumble says he just "made up" as it was time for a last name that began with "T."
Nevertheless, there may have been some perverse cruelty in Bumble because the word "twist" is a slang term for "hanging." Certainly Oliver's last name can suggest different things connected to hanging: a body twisting and writing as the person hangs, the strands of rope that are twisted in a noose, and the rope noose itself that is twisted around the neck of the criminal.
At any rate, giving Oliver the last name of "Twist" seems to place an imaginary brand upon the boy, as others such as the Artful Dodger and Fagin and assign him a criminal role to play. Also, attaching Twist to Oliver places him in many different positions in his life, most of which turn his life in a changing direction. In the end, the happiest twist, or turn, in Oliver's life is his adoption by Mr. Brownlow who
...fill[s] the mind of his adopted child with stores of knowledge, and becoming attached to him, more and more, as his nature developed itself, and showed the thriving seeds of all he wished him to become....
Ironically, it is the other characters who end up with the twist of the rope around them: Sikes inadvertently hangs himself as he tries to escape capture, and Fagin meets the hangman's noose at Newgate Prison.