Ultra Q was the name of the show that preceded Ultraman. It was the first show Tsuburaya Productions produced. Unlike its successors, Ultra Q did not deal with an alien super-hero. Instead, it was a cross between the miscellaneous Japanese monster movies and the American shows The Twilight Zone and The Outer Limits, with a slight mix of The X Files thrown in for good measure. Ultra Q involved the exploits of a pilot & science fiction writer, a news photographer, and an Air Service pilot investigating strange phenomena and raging monsters.
As a result, there was no "Ultraman" named "Ultra Q." Ultra Q did, however, contribute several monsters, including the most famous, Garamon, who appeared twice in Ultraman (called "Pigmon" therein, and reduced to human size), once in Ultraseven, and as a robot helper/comic relief in the animated The Ultraman.
The name "Ultra Q" was a take-off from a phrase used in the 1964 Japanese olympics. There an "Ultra C" was a difficult or complex move. The show, originally called "Unbalance," was renamed "Ultra Q," as it dealt with difficult or complex questions.
As a side note, in the 90's Tsuburaya Productions recreated Ultra Q in movie form for modern audiences. Long-time fans of Ultraman and Ultraseven might recognize the actors playing three detectives investigating the murders that form the centerpiece of the movie's plot. They are Susume Kurobe (Hayata from Ultraman), Shoji Kobayashi (Captain Muramatsu from Ultraman) and Sandaiyu Dokumamushi (Arashi from Ultraman, and Furuhashi from Ultraseven ... he used to be known as Iyoshi or Ikichi Ishii). Coincidentally, the original series featured Hiroko Sakurai, who would later play Akiko Fuji in the Ultraman series.