Such a person would be called a Social Democrat, examples of successful Social Democracies can be found in countries following the Nordic Model.
Put Simply, Socialism and Communism are economic systems, systems which could be blended with any number of political control mechanisms: Authoritarianism, Democracy, Republic, Absolute Monarchy, Constitutional Monarchy,etc.
For example, many Arab states could be called Socialist Monarchies: Qatar, Kuwait, and Saudi Arabia to name a few. Although, few would profess to be practicing such, in terms of State distribution and control of wealth, it is more or less akin to a blended form of benevolent socialism distributed through a welfare state.
Who says communism has failed? Cuba has some of the best healthcare in the third world, their medical schools are some of the best in the region. Life expectancy in Cuba is higher than in many other nations.
Arguably less famine, and suffering exist in socialist republics/democracies than in Authoritarian systems, in that, with absolute power comes inequality, and mismanagement, for an example see Canada, or Ecuador, Vs. Lao, Cambodia, China, and the USSR.