It depends on how you define 'notable' really. In terms of emperors, the last pagan emperor was Julian (361-3), but this is I think quite misleading. Plenty of public officials continued to practise paganism without too much trouble, especially as some emperors/usurpers (such as Valentinian I and the usurper Eugenius) weren't too concerned about people's religious beliefs. The best example would be the court orator Claudian, who was a pagan active in the early fifth century but was also perfectly okay with delivering panegyrics to the Christian Emperor Honorius. There were numerous laws against paganism throughout this period, but they were evidently terribly enforced and did not cover all aspects of pagan beliefs. For more general surveys of why dividing people into pagans and Christians is not very useful, you might be interested in my answers here and here.

In the early sixth century though it is possible to identify a 'final' break with the past, as it would appear that the Praetorian Prefect of 532, Phocas, was the last pagan to achieve such a high office (it basically meant he was the head of the bureaucracy in Constantinople). He was later caught up in the anti-pagan purge of the 540s, marking perhaps the end of politically important pagans in Constantinople. The problem however is that accusations of paganism also made for an easy way to get rid of your opponents, so was Phocas really a pagan or was this a trumped up charge made up by Emperor Justinian to get rid of an influential ex-official? Rumours about pagans were often used by people's political enemies to attack important individuals, such as against John the Cappadocian and Tribonian, two individuals key to the regime of Justinian. In the late sixth century an accusation was even levelled against the patriarch of Antioch! Regardless, it is clear that there was an atmosphere in which people considered it likely that there could pagans within the government. In this case, as Phocas' paganism was attested to in multiple early sources, he is as good a choice as any for the last notable believer in Greco-Roman paganism in the empire.

As a bonus, there is a possibility that one of the last Greek classicising historians of this period, Procopius (active in the early 550s), was a pagan. At least, that's the view of Anthony Kaldellis, who sees the historian as a crypto-pagan revolutionary. Procopius is a super-important source for the early sixth century, so if he was a pagan (which is very very very unlikely), it raises quite a few questions about the Roman Empire at this point. The latest confirmed pagan historian is Zosimus, a former bureaucrat active in the early sixth century who was also based in Constantinople.