The majority of non-monarchic parliamentary systems still have a separate chief of state and head of government (including semi-presidential systems, which are basically parliamentary democracies but the chief of state has a wider set of formal powers without being head of government).
In the EU, for instance, excluding monarchies and presidential systems, every single member state fits the pattern of having a separate chief of state and head of government, mostly with the same titles. Here's a list of EU states that aren't monarchies or presidential systems, identifying whether they are parliamentary or semi-presidential and, if the separated CoS and HoG have titles other than the most common, what those titles are. Unless noted, in the examples, the usual English title of the CoS is "President" and the HoG is "Prime Minister", exceptions have the HoG title in parens (there are not exceptions for the CoS title.)
The majority of non-monarchic parliamentary systems still have a separate chief of state and head of government (including semi-presidential systems, which are basically parliamentary democracies but the chief of state has a wider set of formal powers without being head of government).
In the EU, for instance, excluding monarchies and presidential systems, every single member state fits the pattern of having a separate chief of state and head of government, mostly with the same titles. Here's a list of EU states that aren't monarchies or presidential systems, identifying whether they are parliamentary or semi-presidential and, if the separated CoS and HoG have titles other than the most common, what those titles are. Unless noted, in the examples, the usual English title of the CoS is "President" and the HoG is "Prime Minister", exceptions have the HoG title in parens (there are not exceptions for the CoS title.)
Austria: Parliamentary (Chancellor), Bulgaria: Parliamentary, Croatia: Parliamentary, Czechia: Parliamentary, Estonia: Parliamentary, Finland: Parliamentary, France: Semi-presidential, Germany: Parliamentary (Chancellor), Greece: Parliamentary, Hungary: Parliamentary, Ireland: Parliamentary (Taoiseach), Italy: Parliamentary, Latvia: Parliamentary, Lithuania: Semi-Presidential, Malta: Parliamentary, Poland: Semi-Presidential, Portugal: Semi-Presidential, Romania: Parliamentary, Slovakia: Parliamentary, Slovenia: Parliamentary