The EU has one of those "ideas" websites where people can post and vote on proposals. (Of course, most proposals are going to go nowhere, but maybe it will put the idea in the head of some bureaucrat somewhere.)

And their idea website already has a proposal posted to rename the European Council and Council of the European, in order to reduce confusion with the Council of Europe: https://futureu.europa.eu/processes/OtherIdeas/f/8/proposals...