Whenever I've researched the history of the Middle East (and Persia and India as well) I've noticed that most states and kingdoms are referred to by the name of the ruling dynasty. So, the Abbasid Caliphate, the Seljuk Sultanate, the Almoravid dynasty, etc. There are some exceptions, but this seems to be a general rule when talking about that region.

I'm curious as to why though, since most "Western" nations are referred to by their geographic location, or primary ethnicity. Is that just how convention dictates Islamic countries are referred to in the west? Or is that how they referred to themselves?

If not, how did Islamic or Arabic states see themselves or refer to themselves? Would a king of Ayyubid Egypt refer to himself as the ruler of Egypt, or of the Ayyubid Dynasty/Kingdom?

When the Abbasids replaced the Umayyads as rulers of the Caliphate, did they see themselves as a new dynasty in control of the same Empire, or as an entirely new state?

How about the people who lived in these places? How did they see themselves? Would a person describe themselves as an Umayyad? If asked by someone from outside, where would someone from the Umayyad Caliphate say they were from?

I guess this is really several questions, but they all tie into how Islamic/Arabic nations and peoples saw themselves. It seems to be different than Western self-designations, but I have no idea if this is how they saw themselves, or if it's a Western imposition.