Court said the horse was named after its champion harness-racing father 'Terror to Love'.
He had followed the "proper regulations" when naming The Terrorist after buying the horse last year.
"You get three choices for names... Quite often you don't get what you want, whether it's someone's name or the way it sounds," Court said.
Harness Racing New Zealand's website has guidelines for naming horses but no rules regarding offensive names.
Court said he and the horse's other owner had considered changing the name after the March 15 attacks, but kept it as they felt using a different one would give the shooter what he wanted.
He compared the issue to the controversy around The Crusaders' name following the terror attacks.
Muslim Association of Canterbury spokesperson Tony Green said he could not understand the choice of name.
Green said it was like parents choosing an offensive name for their child.
He referenced a 2012 Internal Affairs report on rejected names for children, including six cases where parents had tried to name their child 'Lucifer'.
"At the end of the day, why would you do that, of all the names in the world?" Green said.