There are a few potential candidates from the sixth century that we know by name, most certainly Zosimus the bureaucrat-turned-historian at the beginning of the century. It is harder to judge who else was definitely a pagan, as accusations of paganism were rife - in 578 even the patriarch of Antioch was accused of taking part in a pagan sacrifice! The same accusations were levelled against prominent officials under Justinian, including Phocas, the prefect first responsible for the construction of the Hagia Sophia. Anthony Kaldellis in recent years has argued consistently for a circle of high-ranking pagans based on these charges and other non-Christian references by the authors of this period. It is unfortunately rather harder to be certain, since it is impossible to ascertain whether they were just Christians who enjoyed classical learning, Christians accused maliciously by their enemies (Justinian was very fond of purging his court), or real pagans. Alan Cameron’s ‘Paganism in Sixth-Century Byzantium’ (2016) takes the most sceptical position and argues for a vibrant circle of Constantinopolitan intellectuals instead, all of whom quite capable of using Neo-Platonic philosophy and ancient myths to burnish their intellectual credentials. I personally find myself somewhere in the middle between Kaldellis and Cameron - for accusations to be credible, there must have been some underlying fear of paganism in the capital that was a least somewhat grounded in reality, even if it is impossible to judge whether the names we have from the sources were really pagans.

In any case, from a contemporary bishop, John of Ephesus, we learn that he had allegedly converted tens of thousands of pagans in Asia Minor. This has its own problems, but no-one I know has seriously disputed this claim. Why is this problematic? Well, bishops across Europe regularly accused the common people of being pagans for centuries afterwards, simply because they performed ‘pagan’ rituals. Unfortunately we also know that ordinary Christians were big fans of magical amulets, curses, astrology, and all manner of rituals that we would not see as fully Christian - yet there is no reason why these people would not have seen themselves as Christians. So when John boasted of his missionary zeal, one has to wonder what kind of ‘pagans’ he had converted (if this was not an outrageous boast of course).

Finally, there is a much later piece of evidence for Roman paganism in the ninth century. According to Constantine VII’s De administrando imperio, there was a pagan community in the Peloponnese until then. Again however we have to be cautious. Although Constantine was careful to say that they were not Slavs, it is unlikely that the local Slavs (who invaded Greece in the seventh century) did not mix with local Romans. Furthermore, this might be another example of an urban intellectual describing rural rituals that he saw as ‘pagan’, but in reality might have been quite Christian. This is the only mention of this group though, so it's impossible to be sure.

As you can hopefully see, answering this question is surprisingly difficult! There is a wide range of evidence, but interpreting them is tricky. After all, how can we hope to understand what was going through someone's head? I personally do not doubt that pagan communities existed long after the sixth century, but direct evidence of their beliefs is simply non-existent. The only ‘evidence’ I can offer is the fact that the surviving literary and documentary evidence do not provide a full coverage of the late Roman/Byzantine world, so who knows what was going on in an isolated corner of the empire. The same beliefs might have been present in the imperial administration itself, but as I argued above, it's never certain - in an increasingly Christian empire, any sensible high-ranking pagan, if they existed, would have hidden their beliefs very well indeed.