Twenty years ago, Paul Crutzen suggested declaring the present a new geological era and naming it the Anthropocene. While this suggestion is still disputed, we argue that the current state of the Earth system is deviating so dynamically from the status quo of the Holocene, that acknowledging a new era has begun is very plausible. However, that leaves open the question if 'Anthropocene' is an appropriate name, since the logic behind it differs from the standard chronostratigraphic terminology. As far as the term is intended to highlight the direct and/or indirect drivers causing the emergence of a new geological era, it could have been baptised as initially 'Populocene' and now 'Consumocene' as first population growth and now growing consumption per capita are the decisive drivers, with the technology providing efficiency gains insufficient to compensate for the impacts of consumption growth. However, behind the prevailing consumption and production patterns and their complex dynamics, capitalism has been identified as the higher-level driver. Some authors argue that the capitalist system depends on permanent economic growth and that the crisis of planetary health can not be overcome without first overcoming capitalism. We argue that this view is based on oversimplifications of economic theory, and that by capping resource consumption by political means, it is possible to steer the economy and society back into the environmental space provided by the planetary boundaries. On the consumption side, this requires a turn to sufficiency-based consumption, facilitated through sufficiency policies protecting and offering access to public goods. However, the impact on the economic system would be profound: not the end of capitalism, but the end of capitalism as we know it.