What function do names serve in the text? Dog woman? Jordan?

Some of the character names in Sexing the Cherry are charactonyms or, in other words, names which reflect the traits of the respective characters.
Jordan is a Hebrew name meaning "one who descends" or, alternatively, "to flow down." This is an appropriate name for this character because as a child, he is pulled from the river Thames by the Dog-Woman. He thus literally flows down the river towards the Dog-Woman, who names him Jordan. This name perhaps symbolizes rebirth, as the river Jordan is associated with baptism in Christianity. It is the river in which John the Baptist baptized Jesus Christ. Therefore, Jordan is an appropriate name for this character, because once he is pulled from the river Thames it is like he is born again, which is the metaphorical meaning of baptism. In Christianity, one is baptized to be cleansed of one's sins and to begin a new life free of sin. When Jordan is pulled from the river Thames, he essentially begins a new life.
The unusually named Dog-Woman is so named in part because she earns a living by breeding fighting dogs. Her name is also appropriate in the sense that she is like a guard dog that guards Jordan. She is fierce and protective.
John Tradescant is, for a time, a gardener for the king. His surname, Tradescant, is a variant of he word Tradescantia, which is a genus of wildflower. His name is thus significant in that it reflects his occupation. It's also significant that the flower his name alludes to is a wild flower. John is also, in a sense, wild in that he is never content to remain within the relatively narrow parameters of his job as a gardener for the king. He always longs to escape to wilder, more exotic places. The character John Tradescant also takes his name, and much of his character, from a real person, John Tradescant the Elder. He was a seventeenth-century English naturalist and gardener, just like his namesake in the novel.
Fortunata's name is, of course, a variant of the word fortune, which can be a synonym for fate. In the story, Fortunata is pursued by Jordan. He imagines that she will complete him, and he imagines that they are destined or fated to be together. Fortunata's name is significant, therefore, in that it reflects what she represents, or for a time seems to represent, to Jordan.