A country states or provinces names are displayed in the online store as it is defined in System > Settings > Internationalization > States / Provinces. States and provinces names in this list are always in English and do not depend on session language.
To localize states and provinces names in the lists displayed in online store, for example on the Checkout screen, you can add new key word-translation pair to a dictionary of the respective language. A value of the Name parameter of a state serves as a key word.
Note: To apply changes, you need to synchronize the online store.