What is the name of the tribe that was part of the San Gabriel mission?

The conventional term used to refer to the Indians who lived in the area where Mission San Gabriel was founded on September 8, 1771 is the Gabrielino Indians. The Indians who were further north and west in the Los Angeles basin, who were in the same linguistic group / tribe were referred to as Fernandinos (after Mission San Fernando Rey).

An alternate name to Gabrielino, preferred by some descents today, is Tongva. I am advised by several experts, however, that there was a limited collective indentity among these Indians, as the residents of each village (there were over fifty villages at the time the Europeans arrived) identified with that village.

You may be looking at mission books. A definitive study of Indian tribes (published in 1978 by the Smithsonian) is Handbook of North American Indians. This large volume has a ten page chapter, Gabrielino, by Lowell John Beam and Charles R. Smith.

If you want to do a serious paper on these Indians you should buy (or find at a library) The First Angelinos: The Gabrielino Indians of Los Angeles by William McCawley. This is the latest study of these indians, published in 1996. It lists for $49.95 but can be purchased on Amazon for about $35.00, less if used.