Tea Cake explains that his real name is Vergible Woods and tells Janie,
De name mah mama gimme is Vergible Woods. Dey calls me Tea Cake for short.
We can infer that people called him Tea Cake because his original name was awkward and hard to pronounce. Janie also realizes that he was given the nickname because he is a sweet or likable person. When she asks him if he is as sweet as his name suggests, he says he might be and says she should try him out and see.
Tea Cake, though a flawed character, is in many ways "sweet" and delightful for Janie. He is young and vibrant and treats her as a human being in a way her first two husbands never did. He encourages her to develop, inspiring and invigorating her with his creative and charismatic personality. He teaches her new things, such as how to shoot a gun. He doesn't force her to follow him to places she doesn't want to go.
However, Tea Cake can also be unhealthy for her. He steals 200 dollars from her, and he is jealous that she will stray from him, which causes him to beat her.
Tea Cake's nickname thus reflects the genuine treat he is for Janie after her experiences with her first two husbands. However, he also, like most sweets, can be unhealthy for her, too.