Furacity

The boys in the band have always kept mum about their sex lives, but audiences don't fail to speculate on the meaning of the animal costumes that dominate their live performances and videos. Although their lyrics are safe for children and work, numerous Furacity fanfic and slash parodies clutter the various Internet forums devoted to their style. The music, peppy teen anthems and slow love ballads written to lovers of indiscriminate gender, is secondary to their popularity.

Marsupial Hermaphrodite with Extra Anatomy in a Pouch

I believe this one was generated through a discussion of actual animal anatomy. It's two band names, the second one being the opener.