To many countries call their HoS "President" and their HoG "Prime minister". Frankly I think it's dull, and a bit sad, it limits creativity and makes many countries look like generic English-speaking republics.
In Barmenia, were we have recently introduced a heredity monarchy, we call our combined HoS/HoG "Potentate". Other replacements for President could be "Consul" (that's a really fine one), "Chancellor", "Tribune", "Director General", "Administrator", "Steward", "Lord/Lady", "Guardian", "Warden", "Governor", "Jarl", "Vizier", "Grand Magister/Magistrix", "Doux" etc. etc. etc. Why does it in so many cases have to be "President", followed by a "Prime minister". Use your imagination and we'll get a lot more cultural activity, and excellent opportunities for RP.
And why does everyone needs to even have a HoG in a republic? The two posts are better merged together.