Tarzan is not a name from any real language. It is a word from a language that one man made up to go with it.
Edgar Rice Burroughs had spent years in unsuccessful jobs and business ventures in Chicago and Idaho, according to Britannica, before he turned to fiction. The first Tarzan story appeared in 1912, and the first Tarzan book, Tarzan of the Apes, followed in 1914. Wikipedia places the debut in the October 1912 issue of All-Story.
In the story, a British nobleman's son is orphaned in Africa and raised by great apes. The apes speak Mangani, a language Burroughs invented and then scattered through the novels. In Mangani, "tar" means white and "zan" means skin. Tarzan is the apes' name for the pale boy, "white skin." His English name is John Clayton, Viscount Greystoke.
The ERBzine fan site, which reproduces Burroughs's own Mangani and English dictionary, lists those two entries. It also shows the logic of the language. A white human is a tarmangani, "white great ape," and a black human is a gomangani. The hero's name is built on the same word for white.
The name was not the first idea. Wikipedia says Burroughs considered "Zantar" and "Tublat Zan" before settling on "Tarzan," and ERBzine says "Zan Tar" was among the first names he considered. None of the sources we read say why he chose the final order.
The name proved valuable. Britannica counts 25 Tarzan books, and Edgar Rice Burroughs, Inc. still claims the name as a trademark, even though Wikipedia notes the copyright on the first novel has expired in the United States and other countries.
Burroughs also named his California ranch Tarzana, and the Los Angeles neighborhood that grew around it kept the name.