"Uhura" comes from the Swahili word uhuru, meaning "freedom". Nichols states in her book 'Beyond Uhura' that the name was inspired by her having had with her a copy of Robert Ruark's book Uhuru on the day she read for the part.
When producer Robert Justman explained to Roddenberry what the word uhuru meant, he changed it to Uhura and adopted that as the character's name.
Coincidentally, the end credits of the film Star Trek VI: The Undiscovered Country incorrectly refer to Uhura as "Uhuru".