What is the correct name for SO3?

The correct name for ##"SO"_3"## is sulfur trioxide.

Using the rules for the nomenclature for naming binary covalent (molecular) compounds, the compound ##"SO"_3"## is named sulfur trioxide. The prefix tri- indicates that the oxygen has a subscript of 3 and that a molecule of sulfur trioxide has three oxygen atoms. In this chemical formula, sulfur does not have a written subscript, which is understood to be 1. You might wonder why it is not called monosulfur dioxide. By convention, chemists do not add the prefix mono- to the name of the first element in the binary covalent compound. However, if the second element has no subscript, it will be given the prefix mono-. For example, the binary covalent compound CO is named carbon monoxide, not carbon oxide, and not monocarbon monoxide.

Comment: "I always get confused on SO3 as a molecular compound and SO3 as a polyatomic ion why are they expressed the same way?" Kaneki

When the compound sulfur trioxide (##"SO"_3"##) is indicated, there won't be a charge associated with the formula. When the sulfite ion is indicated, it will have a charge of 2- associated with it (##"SO"_3^"2-"##).