[aguaviva]

What connotation is that exactly?

The connotation of intentionally ignoring their very, very, very clearly stated preference as to what their official name is. Neither of these countries refer to themselves as "The Congo" as such, and they've made it known that they would prefer that you not do so as well. That's all there is to it.

"Use case" has nothing to do with it,

Au contraire. Language is all about use cases.

It's use cases über alles, in fact.