Captain Saavik: Saavik is the first Vulcan woman introduced in Star Trek who's name did not follow the " T' " convention (The T' prefix being the contraction of the word T'sai, meaning "lady" in Vulkhansu).
That is due to the fact that her name is in fact a Romulan name, meaning "Little Cat" in Rhiannsu. The name Saavik does also exist in Vulcan, but is a traditionally male name coming from the words sa’ahkh-vik, meaning "From the well-war" and referring to the ancient conflicts around wells and water sources in the Forge.
Saavik is said to be of Spock's clan as of the time of ST: Eridani, and if we follow the clan name given to him in the novel Ishmael, her full name would be S'chn T'gai Saavik, with S'chn coming from the words s’khart-lan, meaning "from the captain" in Vulkhansu, and T'Gai, coming from the words t’sai gadzhai, meaning "lady of the feast". That usage has however yet to be seen in the Alpha Canon of Star Trek.
David James Marcus: David is a name of hebrew origin, meaning "To love" or "Beloved". It is worth of note that another Star Trek character shares this name, David McCoy, Leonard H. McCoy's father, and subsequently, Joanna McCoy's grandfather.
David Marcus' middle name, James, was first confirmed in the book Star Trek II: Biographies. That implies that despite Carol Marcus' wish to raise her son on her own, she still gave him his father's name as a middle name. The name James is of Hebrew and Latin origins, and has the meaning "supplanter", "seized-by-the-heel" and "may he protect".
Marcus is a latin name, meaning "Dedicated to Mars", the god of war, or "Warlike". It was greatly used in Roman history and survived beyond the Roman Empire.
Joanna Eleonora McCoy: The name Joanna is derived from Greek, Hebrew and Latin, and means "God is gracious". In-Universe, it was a Hall family name, and was ultimately chosen by Jocelyn.
Eleonora on the other hand, while continuing the tradition of weird McCoy's middle name, was chosen by Leonard, as his own grandmother was name Eleanor. Eleonora is a derived name coming from the Old Provençal French Aliénor, having among it's meaning "light", "brilliant" and "Merciful", and the name Aliénor is also descended from the Greek name Helen.
McCoy is a last name of Scottish and Irish origin, and is the anglicised version of "son of Aodh", a deity connected with fire.