So I know that most Patrician families disappear from the records in the East around the 7th-8th century. While their disappearance in the West makes sense due to the collapse, I'm wondering what could have led to the same thing in the East, where Constantinople remained unconquered until the 13th century.
I actually go into it extensively in this older post.
But in a nutshell, the decline of surnames in both empires is due to the decline of necessity of extended lineage as a means of social advancement. I say extended because families have always mattered, but for the survival of surnames, you need to have a reason for tracking family lineages past immediate memory, meaning beyond 2-3 generations.
The reasons for disappearance in the West is because of the collapse of the imperial state and bureaucracy. The reasons for disappearance in the east because of the complete restructuring of the imperial state and bureaucracy from a predominantly aristocratic civilian system to a slightly more meritocratic military system (militaries have a low tolerance for long-term nepotism in times of grave crisis).
Though Constantinople was around this whole time, its bureaucratic and military system was not static. It had to adapt and change completely to survive very trying times.