It depends on the circumstances and the sect.
If we are talking religiously, the terms used are: Caliph, Mullah, Sheikh, Ayatollah (Shiites Only), etc.
If we are talking politically, the terms used are: Sultan, King, Emir, etc.
The name of the ruler of a Muslim country depends of the country constitution and the ruling system. The name could be, as an example, King, President, Sultan, or Prince (or Amir in Arabic).
God through Koran and prophet Muhammad (PBUH)
Amir, khalifa, sultan, king, sheikh, president, or imam
There is no leader of the Muslims, it's a religion not a social group.
Emir
A caliph.
sultan
I think the term you are looking for is caliphate, and the ruler was called a caliph.
The Muslim ruler, Akbar, mandated religious and cultural toleration.
Muslim Ruler.
Chief or ruler of a Narragansett territory
sultans
Muslim Ruler.
Humayun
Mali has had numerous Muslim leaders. Perhaps the most famous was Mansa Musa, who was a ruler of Mali during the 1300s. He embarked on a holy trip to the Muslim city of Mecca in 1324.
Emir - Title of a Muslim (Mostly Arabic) ruler.
Because their ruler wanted to convert Ghana's ruler to a Muslim.
Sultanate.
Mohammad Ghori