The best source for information on the history of backgammon and variations
from around the world (that I am aware of) is H.J.R. Murray's "History of
Boardgames Other than Chess" (1952). A version of the modern game was
played in Spain in the 16th c., except that there was no such thing as a
gammon and doubles were not played twice. This game was called "todas
tablas" (in France, it was "toutes tables"). The addition of gammons and
playing doubles twice occurred early in the 17th c., and this version was
called "tablas reales" in Spain.
There were also many other variations that involved different starting
positions. One characteristic of these variants is that three dice were
often used instead of two. Examples from Spain include cab e equinal,
fallas and emperador. These games were also played in other countries
under similar names and date back to the middle ages. It's possible but
uncertain whether they were still played in the 16th century.
The generic term for backgammon was tables in English, tablas in Spanish,
taules in Provencal, tables in French, tavole in Italian, tabulae in Latin.
A single piece was called a "tablero" in Spanish and a "taulier" in
Provencal("tableman" in English).