Depends on the level of development of Communism, and we won't know what is applicable to when until we get there. Communism isn't a Utopia invented by Marx, but a prediction for the future based on analysis of politics and economics throughout history and the present, ergo we have to develop into it and see where it actually takes us.

In general, though, with a fully publicly owned and planned economy, people would be rewarded for their labor, yes, but it might take the form of labor vouchers, a different form of currency, etc designed to not be transferable to others in the economy individually, but with the social fund as a whole. This system of varying "prices" can be solved for using various feedback loops called "cybernetiks."

I recommend reading Prices in a Planned Economy, it's a useful intro to how to think about abolishing the commodity form.