It's also sometimes called तिल (til), which is more commonly used for sesame seeds, but can sometimes refer to flax seeds.
Here are some other regional names:
* ತುಳಸಿ ಬೀಜ (tulasi bija) in Kannada
* அலசம் விதை (alasaam vidai) in Tamil
* అలసందలు (alasandalu) in Telugu
* അവ്സൻ വിത്ത് (avsan vitt) in Malayalam
The specific name used may vary depending on the region and dialect.