Discussing various philosophers is no different than discussing philosophy. Some philosophers spent most of their time discussing a particular topic such as God that they became known for that topic. Other philosophers discussed almost everything. Philosophers come from particular cultures, times and languages. Philosophers can belong to a philosophical school. Philosophers can even be known to the wider world for something other than their philosophy.
It is for this reason that there are different ways to talk about various philosophers. The primary way to speak about a philosopher is historically. If we want to discuss Aristotle, then we discuss him as he fits into his ancient Greek context. We discuss what influenced him both philosophically and otherwise. We also talk about what he did that influenced the later course of history. We certainly mention what he believed and why he believed it. This is the most important and primary way of speaking about a philosopher.
We can also speak about a philosopher in a secondary way. When we are talking about Aristotle, we might speak of Protagoras because Aristotle disagrees with him. It might be that Aristotle does not properly represent Protagoras, so this is a secondary way of speaking about him. Another secondary way of speaking about a philosopher is by mentioning his philosophical opinion on some issue. For example, both Aristotle and Thomas Reid believe in libertarian freedom. The problem is that they believe in libertarian freedom for different reasons and place a different level of importance on that issue. Yet another secondary way of speaking of a philosopher is by school. A school is a set of beliefs that a bunch of philosophers all agree on and label themselves by. So Thomas Aquinas and Averroes were both Aristotelians, but their philosophies were very different. There are many other secondary ways that particular philosophers might be discussed such as culturally, regionally and religiously, but the previous ones are the most important.
Since speaking historically of various philosophers in the most important way of identifying them, they must be identified the same way that any historical group of people are identified. Generally, we refer to the culture, time, nationality and region in order to narrow down historical figures. So Aristotle was Greek, lived from 384-322BC, was Macedonian and lived in or around Athens. In general, it seems best to refer to three general time periods: Ancient, Medieval and Modern. It also seems best to use national regions to refer to philosophers by place. Since nationalities change over time, time periods will take precedence over national regions. Ancient philosophers have different beginnings in different places and end approximately around 400-500AD. Medieval philosophers end at around 1500AD. Modern philosophers continue from Medieval ones until the present. We can further divide philosophers by region. We have Western philosophers who came from Europe and the Middle East, Eastern philosophers that came from China and the East Asian countries and Indian philosophers. Other regions never had any philosophers until much later on when they joined one of these traditions.
This divides philosophers into nine areas: Ancient Western, Medieval Western, Modern Western, Ancient Indian, Medieval Indian, Modern Indian, Ancient Eastern, Medieval Eastern and Modern Eastern. Since philosophers write much of philosophy, this also divides philosophy into into the same categories.