Uhura's name was derived from "Uhuru," the Swahili word for "freedom." Spock, after making a Vulcan mind meld with Kollos, says that Uhura's name means "freedom" and recites a line of poetry about beauty from Lord Byron.
The character's given name was never established in the series or the movies. In Star Trek VI, her name was misspelled "Uhuru" in the credits. By the early 1970s, fans had suggested that her first name may have been "Penda", meaning "love". Later, the name "Nyota" ("star" in Swahili) became more commonly used, first by William Rotsler in his book Star Trek II Biographies.
Nichols has said that an author writing about the history of Star Trek had asked Gene Roddenberry what Uhura's first name was and was told that one was never decided. The author then recommended the name "Nyota." Roddenberry liked it, but said to ask Nichols before he allowed the name to be used. Nichols thought the name was perfect. (TOS Season 2 DVD commentary)
In the Star Trek RPG published by FASA in the 1980s, the full name given for Uhura was "Samara Uhura," although, like the rest of this game, its source material was stricken from canonical status after the debut of Star Trek: The Next Generation and Paramount Pictures revised canon policies. This possible name appears to not have been accepted outside the original source. Ironically, in the The RPG adaptation, there were several Decker-class starships named for the Enterprise crew, including the USS Samara Uhura.
http://memory-alpha.org/en/wiki/Uhura#Name_and_heritage