The Connection Manager in QT, for example, is not a Connection Pool. It's more of an interface to get at all the classes that represent real things within a connection process (requests, responses, active connections, etc). There is no information in the Connection Manager except system/process defaults. The Connection Manager would create connection pools if that is what's needed but it isn't Connection Pool any more than it is a connection.

That said, I sympathize with the impulse that the term "manager" says there's something wrong in your OO design. It is simply that determining how to get around the problem is hard.