Yes, there’s definitely a significance to Little Bee’s nickname in the story. This is because Bee, whose name we discover at the end of the novel is actually Udo, takes on her moniker after escaping a brutal attack that wiped out her entire family and village. Little Bee’s adoption of a new name serves both two purposes: to hide her old identity from any would-be dangers and to mentally cope with the tremendous horrors she’s suffered prior to arriving in Britain.
Little Bee seeks asylum not only from her new country, but from a new name. Taking on a superhero name makes her emotionally stronger and better able to subdue the memories of her family members’ deaths. This is the same adoption of a new identity that we witness in Charlie, who delves into the character of Batman to cope with his father's depression and later death. A new identity makes Charlie feel less powerless against the "baddies" of the world, just like Little Bee's makes her more able to battle the evils she herself has witnessed.
"Little Bee is only my superhero name. I have a real name too, like you have, Charlie" (129)
Bee also drops her tribal name out of fear of retribution. Throughout the novel, Little Bee is resigned to the fact that Death seems to follow her. When she arrives in a new place, she makes a point of determining how she would commit suicide there. She does this not out of a desire to die, but to prevent the same death her sister suffered from happening to her. As another preventative measure, Little Bee discards her tribal name Udo, lest some stranger recognize where and what exactly she escaped from in Nigeria. As the only surviving witness to the massacre of her village, Bee would be in very real danger should she ever be discovered. Because of her past, she becomes an expert at hiding her true identity.
Udo is haunted by what happened in Nigeria, and it is both a means of mentally escaping those horrors and hiding from any possible danger that she adopts the unusual nickname Little Bee.