The Buddha had many names — Siddhartha, his given name; Gautama (or Gotama), his mother's clan name, which he used when he was an ascetic; Sakyamuni (or Shakyamuni), "Sage of the Sakya [tribe]," a name used by people around the world; the Buddha, "the Awakened One," used after attaining Enlightenment — but the one he used to refer to himself most often was the Tathagata.

"Tathagata" (the same in both Sanskrit and Pali) is a term used to refer to the Buddha as a spiritual principle and not as a person or title. Specifically, "Tathagata" refers to a person who has attained full Enlightenment and escaped samsara. Sakyamuni Buddha used it to refer to himself often, and also used it to talk of the Buddhas of previous kalpas and kalpas to come.

The actual definition of the term is a bit hard to pin down. Tatha means "so/thus/in this way" (like the French ainsi). Gata is the past participle of "to go." Combining the two, we get the phrase seen often in translations: "the Thus-Gone one." This reflects the idea that the Tathagata is not to be born again in this world — that he has left the cycle of rebirth, and is "gone." In referring to how a bird leaves a ship for good when land is nearby, the bird is said to be "tathagatako." Buddhaghosa, in his commentaries of Buddhist texts, lists eight ways the word might be interpreted.


References:
The Tathagata is "Truly Gone": http://www.dharma.org/ij/archives/1996b/ss_gone.htm

Tathagata is the name that Buddha said people should use to refer to him while he is still alive. When somebody attains a Perfect Enlightenment, he calls himself as Tathagata, which means that he is the one who has opened his eye completely to the world. A Tathagata appears in the world once about every 3000 years. His mission is to reveal the way of the world for all mankind.

 

People who have attained Supreme Enlightenment and named themselves Tathagata:

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