To some extent, each den is unique and crafted to suit the needs of the individual animal. So each one could be called unique, potentially. We have also seen evidence of "locality" among certain species, where beavers pick up different techniques from their parents or neighbors when building and re-building dams. Or where bears teach each other tricks to get around human habitation.

But I don't know if I would go so far as to call it a style... I think "style" implies an ideal of fashion or values. There would have to be a clear idea of good or bad examples in order to decorate properly. It feels a bit too far outside of function to have a strong presence in non-domesticated animals. Even animals like rats (which are fastidious about their homes and re-arrange daily or weekly), the arranging part is still largely functional, changing pathways, access points, cleanliness, or textures.

So, to answer your question, I think "style" is a purely human concept. However, plenty of individuals animals DO have a preferred form of building and maintaining dens, and that is something we see across many species. Each animal is going to have its own unique method of going about things and its own way of meeting needs. The way they change and decorate the den is probably going to be a reflection of that rather than a particular "look".