Copied from this page: http://myth.bungie.org/legends/relics/mythology.html
Chris Stelnick believes Shiva is actually an allusion to Shiver.
"...I believe Shiva is more like the Fallen Lord Shiver for several reasons.
A) Shiva is a female, as Shiver is
B) Shiva used strong magical powers as we have seen in very old RPGs as Shiver uses her Dream spells to fight and ultimately loses with the spells
C)Shiver and Shiva...a very similar spelling
D) Balor uses Lightning as his main magic which would not match up with Shiva's Ice spells from the RPGs"
Not substantial but there's a lot more info on Shiva on that page.