K9
There is little doubt that Bob Baker and Dave Martin intended for their creation to be known as K9. This is readily apparent from PDFs of contemporary 1970s documents available on the "classic" section of the official Doctor Who website. It is also evident in the fact that he is consistently styled "K9" in Target Books novelisations, such as, to pick a random example, Doctor Who and the Stones of Blood. Stories in the 1983 K9 Annual also avoided hyphens, as did contemporary children's fiction like K9 and the Beasts of Vega. The hyphen was also absent from some later, original novels — like The Well-Mannered War. The style "K-9" was never used in any credit sequence of the 1970s or 1980s, and has generally (but not entirely) been avoided in BBC Wales productions. During the 1963 version of the show, K9 was only credited once in any way other than "K9", and that was in Full Circle, where John Leeson was credited as the "Voice of K.9".
This authorial intent has been carried through to the present day, where the K9 TV series, of which Baker is the co-creator and associate producer, also uses exclusively a hyphen-less approach to the name. Neither the show's official website, nor is Network Ten advertisements, use anything other than K9 as a way to style the name.
So, if all that's true, where, then, do we get the seemingly popular "K-9"? Doctor Who Weekly. The original editor, Dez Skinn — perhaps mistaking for a hyphen the little "dot" between the "K" and the "9" on the dog's bodywork — allowed the use of the hyphen in some of the very earliest Fourth Doctor comic stories in that magazine, and the hyphen stuck, as far as Doctor Who Magazine was concerned. It became a part of the "house style" of that magazine to write the name, "K-9". Fandom followed suit. As fans grew up and became part of the professional "industry" of Doctor Who, "K-9" gained some, but not universal, traction.
Thus you will find some 1980s and 1990s fiction (like, for instance, the short story "Housewarming" and the novel Interference) which use "K-9". You will also find "K-9" used in the synopses printed on the covers of DVD releases. The Region 2 release of Full Circle, for examples, uses "K-9" in this way. And it's likely that we will occasionally still see "K-9" in future fiction, depending upon the age of the author, the preferences of the publisher, and other somewhat arbitrary factors.
Still, conforming to the general T:NAMING rule that the more common names shall apply, the rule we've adopted here is that K9 "wins". Though "K-9" may be more familiar to some fans, "K9" is entirely more common in terms of the number of uses in credits, number of uses in the body of fictional works, and in terms of the two occasions in which K9 has headlined his own shows.
By writing this policy, we're not failing to acknowledge the legitimacy of arguments which might be constructed to defend the "K-9" rendering. We're merely saying that for stylistic purposes, it's important to pick one spelling and stick to it.