The Olmecs called themselves Xi (Shi)

We know the name of the Olmec from the Maya. Landa noted that the Yucatec Maya claimed that they got writing from a group of foreigners called Tutul Xiu from Nonoulco (Tozzer, 1941).

The Olmec originated writing in Mexico, so we can assume that the term Tutul Xiu refer to the Olmec.The Tutul Xi were probably Olmecs.

The term Tutul Xiu, can be translated into Olmec which is a member of the Manding Superfamily of languages as follows:Tutul, "Very good subjects of the Order".Xiu, "The Shi (/the race)".

These terms together would read: "The Shis (who) are very good Subjects of the cult-Order".

The term Shi, is probably related to the Manding term Si, which was also used as an ethnonym. Since Si/Xi was used as an ethnonym, the Tutul Xi-u were the Olmec people. Thus I call them by their own name Xi.

Reference:

Landa, D. de. (1978). Yucatan before and after the Conquest. (Trans. by) William Gates. New York: Dover Publications.