OpenWhisperSystems really made clear in various places that they do not want any other Signal binaries than the ones signed by them to access their servers. So far, F-Droid respected this request.
If you want to publish a branded version of Signal, one point is the one you already mentioned, giving it another name. The other point is that you must change the server the app is accessing, thus making it unusable to chat with Signal users. Imho, the already existing users are the only advantage over other solutions like Matrix or XMPP/Jabber, therefore this branded version would not make much sense.
See also: