As I know , the original name , when it was a product of META & then acquired by Avant! , it was called " HSPICE ".
After Avant! had had it , the name became " Star-HSPICE " . The reason MAY be to just change & inform of a new brand ( someone correct for me if it is not true " Avant! had had also some products named Star-..... ).
After Synopsys acquired Avant! , the name still as was.