In Star Trek history, Klingon ships never had any designations whatsoever during TOS, they were only ever referred to as Klingon Battlecruisers.
During the Animated Series, while trying to identify a Klingon Battlecruiser, Spock makes reference to one of them being a Klolode class Battlecruiser with the implication that there also existed also classes of Battlecruisers. The Klolode class was considered equivalent to the Constitution class Enterprise of the Original (and Animated) series. No reference was made to any nomenclature, still, however.
The first useage of Klingon ship designations did not in fact, come from any canon source at all, but does in fact come from Starfleet Battles and fan fiction, where the term D7 Battlecruiser was used to describe the Klolode class. The term became so popular that it found its way into much Trek fiction, and was expanded upon by SFB to include D6, D5, E5, E4, and so on.
When Star Trek, the Motion Picture was released in 1979, the movie itself still made no direct reference to the class of Klingon Battlecruisers shown fighting V'ger in the beginning, but in the script and movie novelisation, they were given the name K'Tingla class.
FASA then released its version of SFB, called the Starship Combat Simulator, based on material from both the Original series and the Movies. Here, they used the same more popular designations such as D7, but also created some new ones, such L24 and so on, remaining consistant with the nomenclature. As far as I can tell, this was just purely creative differentiation or artistic license to make their product different from SFB. The FASA designations were not picked up by any other Trek fiction, nor by Paramount, to the best of my knowledge, however, Paramount did actually pick up the D7 designation and in an episode of Deep Space Nine, Sisko refers to a Klingon ship as a "D7 Battlectuiser". This has actually stood as an example of where fan created material has actually become cannon through popularity.