Assuming the Clans are even aware of Kipling's work. They have almost zero written stories/histories outside of their Remembrances. I think this link might be a wee bit of a stretch.
I'll grant that Warriors of Kerensky claims that "literature is almost unknown in the Clans" with the few books in circulation written post-Exodus and heavily censored. However, much of what was in Warriors of Kerensky has been superseded by later texts. Notably, the very next paragraph in WoK notes that many tales shared in the Clan oral tradition are parables, often plagarized from Inner Sphere sources and changed to reflect the Clan viewpoint. So it would fit that the tale of Rikki-Tikki-Tavi might be orally passed on to sibkos in the creche, even without printouts of its text, with a focus on the importance of defending one's family against the plots of those who seek to seize one's home." Rikki-Tikki-Tavi features a warrior animal, multiple killings, and a shotgun blast to the face - all good bedtime story material for li'l Clanners.
The Falcons purged their books and other historical records, but they seem to have been outliers in this regard. The Cloud Cobras retain large libraries of religious texts, and the Goliath Scorpions were notorious hoarders of historical artifacts (literature included). Jaime Wolf, when visiting the Gray Death Legion on Glengarry, sought to fight a re-enactment of Gettysburg. Without historical texts, why would he have cared about such an ancient battle? Sure, he could have picked it up during his decades in the Inner Sphere, but without prior context, what would be his motivation?
One can infer that the Coyotes (and the Scientist caste, in general) had access to significant amounts of historical literature. Otherwise, what meaning would a "labname" have, linking them to a famous scientist, if they knew nothing of history?
Nonetheless, the name's less important than what it clarifies - the species. It wasn't clear from the art, but the name pretty solidly establishes the two as mongooses (as opposed to ferrets or otters). It's notable because the other Spaniels are explicitly not from Clan totem animals. (And would the inclusion of the mongooses be triggering for members of Clan Cloud Cobra?)
