Foolestroupe,
It's not called a chromatic dulcimer because there are already lots of instruments that are tuned in the traditional pattern that have been made chromatic. They have been called chromatic dulcimers for years. Besides, the tuning of the piano dulcimer is very linear, like the tuning on a piano. The scale pattern even follows, in a way, the expected pattern of white and black notes.

Kaleea,

Persia = santur
Indai = santoor
China = yang ch'in
Greece = santouri
Germany = hackbrett
Hungary = cymbalom

JP