The Tamil meaning of Anai is correct (see e.g.
http://en.wikipedia.org/wiki/Annamalai_Hills for an internet resource), though I have no idea whether it gives rise to Anaya. To the best of my knowledge, the name does not derive from Sanskrit: see
http://www.behindthename.com/bb/arcview.php?id=215016&board=gen.
The Hebrew meaning is attested in prior posts on this board. See e.g.
http://www.behindthename.com/bb/arcview.php?id=198434&board=gen.
The use in Spain was also mentioned (see e.g.
http://www.behindthename.com/bb/arcview.php?id=312730&board=gen), though the Basque origin and meaning I do not know.