This is something important to consider when making your own Clan. Are these cats related to the canon Clans? Perhaps some rogues and kittypets wanted to make an organized, functioning group. Backstories are important because certain elements of it can always be alluded to in causal conversation among that Clan's cats. This makes your story and Clans seem more developed and constructed.
Also, don't forget Clan lore! Does your Clan have any stories about great victories or losses? You can also make your Clan have special traditions exclusive to them.