Which company manufactures the air data system on the Boeing 787-9 'Dreamliner'
Boeing procured the avionics for the B787 in "packages". Air data was part of the "Navigation Package" which included in addition to air data, IRUs, nav radios, GPS sensors, and the FMS software.  

Honeywell was selected as the supplier for the Nav package. So they provided the air data system.  I don't know what specific system they supplied.