Some associations allow all and any pets. Some will allow one pet, some more. Some condos allow a small dog under a certain weight; many allow one or two indoor cats. Most condo associations allow small caged pets like gerbils, hamsters, fish, and reptiles. But don't assume that any particular condo complex allows any pets at all.
Naming a complex is the first step in branding it, so developers take their time about naming their projects. They want the perfect name to attract the perfect buyers. The name is the first thing that indicates to a buyer whether the community is right for them, and developers need their projects moniker to say, "Why yes, this is the perfect spot for you to drop several hundred thousand dollars!".