I sometimes do rebranding exercises for companies that already exist (eg. a new design for their website, a new logo, etc) but they're uncommissioned and done without asking for permission. Is it okay for me to show these rebranding concepts online or would there be copyright issues? I make no money from it.
What you do on your own is on your own - but the moment you start showing it, it than enters the public realm. And once it enters the public realm, legal frameworks are applied. At this point, what's legal and what's not becomes a negotiation between you, the public, the government, and other entities that may have a vested business interest in protecting their image and depiction in the public sphere. So now the question becomes "Do I have the resources (time, money, legal representation) to protect my creative work, even if it's somewhat derivative of others work, inside the legal framework of the region I work in?"
And to answer that question may require the trained skills of a legal representative.