Really depends on the language. In most cases, particularly fron African-American names such as
LaToya, "la" is the female form of the French "le" meaning "the".
Another case includes Greek names beginning with La such as Laodice. Such names are related with "laos" meaning "people". "Laos" itself is derived from "laas" meaning "stone". Why on earth is "people" derived from "stone" you might ask?
We have to go back to Deucalion, who is to Greek mythology what
Noah is to Hebrew mythology: Very much like
Yahweh,
Zeus was once pretty pissed-off by the disrespect shown by humans and punished them with death by flooding.
Prometheus was able to warn two humans, Deucalion and his wife Pyrrha. They floated on the flood in an ark which they had made until the floodwaters abated. Then they went to a temple of
Themis (
Prometheus' mother) and begged her to help them restore the human race. She old them to do so by throwing stones ("laas") of the earth or
Gaia over their shoulders. So they they began to pick them up from the ground and throw them over their shoulder: Every time a stone struck the ground which Deucalion had thrown in formed a man. Each stone of Pyrrha's which struck the ground became a woman. In this way the human race ("laos")was reborn.