The Stoics, named after the Stoa poikilê ('painted porch') where the school's founder Zeno of Citium taught, where also known as the Zenonian school in antiquity. Stoicism is a modern word. The periodization of the Stoic school which I use here is also not ancient (unlike the periodization of Plato's Academy, say).
The Stoics were the dominant school of philosophy in the Hellenistic period, their ideas had a significant impact on the revivals of Aristotelian and Platonic philosophy in the Roman period, and even after Plotinus' successors ("Neoplatonism") became unquestionably the most important school, non-philosophers were still often closer to the Stoic-based philosophical koine ('shared discourse') than to Platonic ideas.
The paintings with which the Stoa poikilê was decorated in the 2nd century CE - long after Zeno - are described by Pausanias.
This group is defined through inclusion in the important fragment collection Stoicorum Veterum Fragmenta by Hans von Arnim.
Zeno of Citium
Cleanthes of Assus
Chrysippus of Soli
This group is defined simply by being neither Early Stoics nor Roman Stoics.
This term is typically used for Stoic philosophers from the time of emperor Augustus onwards, although Stoics had been living under Roman rule and in Rome itself for some time before this. There were still Stoics in the latter half of the third century CE, but I don't believe there is clear evidence of Stoic philosophy being taught later than this.
Chaeremon of Alexandria