Jindal's first name is Piyush. And Haley's maiden name is Nimrata Randhawa. So yeah, they both Anglicized their names. Would the Democrat's message be more palatable if he went by the name Chuck Taj?
By not changing his name, he demands that his host country adapt to him. Haley and Jindal chose to adapt to America. Anglicizing ones name may seem insignificant to some, but it is actually very important in a nation where the illegal invaders think that they can force us all to learn Spanish.
His message would still be foolish if he did Anglicize his name, of course, but not Anglicizing his name is typical of a person who wants to force everyone to conform with his Stalinist ideals.