PROVIDENCE - Rhode Island residents will vote next year whether to shorten the state’s longest-in-the-nation formal name because of its association with slavery, state lawmakers decided yesterday.

Officially, Rhode Island is called “The State of Rhode Island and Providence Plantations,’’ which some say conjures painful images of slavery in a state whose captains once grew wealthy off the trans-Atlantic slave trade. Critics of the move to shorten the state’s formal moniker argue the unwieldy name merely shows how several settlements merged into one colony.

After years of debate, House lawmakers decided yesterday to approve a referendum allowing voters to decide whether to delete “Providence Plantations’’ from the name. The Senate approved the measure this year.