The term "monster dog" is not the "official name" of this animal; however, it is consistently used by Visual Effects Supervisor Ken Ralston during an interview in the Star Trek III: The Search for Spock (Special Edition) DVD, which discusses the creation of the puppet.
Arthur C. Clarke spoke fondly of this creature, remarking, "It seemed to embody the best attributes of a German shepherd and an alligator." However, A.C. Crispin was much less enthusiastic about the animal, commenting, "Will somebody please tell me what the Commander's pooch actually ate? Kruge's alligator-dog seemed to me gratuitous, something that ILM toted in as an afterthought, possibly a mechanical marvel left over from the critters fashioned for Jabba the Hutt's entourage [in the Star Wars film Return of the Jedi]. 'Hutt's Best Friend,' so to speak." (Starlog, issue 88, pp. 35 & 36)
In the Universal Studios Hollywood theme park's Star Trek Adventure experience, a child participant would be selected to play a similar Klingon pet in each presentation. In the closing credits of the edited "episode," this juvenile creature was called a "puppy lizard."
In the Star Trek III: Starship Combat Game, the creature was a jadashha.