A democratic system in which the named "ruler" is a symbolic head of state, and power rests in the hands of elected officials.

democracy

monarchy

constitutional monarchy

democratic socialism

The best option here is constitutional monarchy.

This ruler would be the monarch: this person then only represents the country, but does not have a say in the government.

An example today is Great Britain, where Elisabeth II is such a ruler. Many other European countries are also constitutional monarchies.