We sort of have that with Sprout Social. Our community is called The Arboretum and has a different logo/color scheme, etc. However, I think the team is interested in bringing it more unified and less of it being it's own separate thing. For folks not close to Sprout they don't know what Arboretum is and now that we're a closed customer community, it makes more sense to be closer to our brand.
I guess, depending on your goals of the community!