The answer is more social than structural, once you reach a certain point. When you're on a rotating planet, obviously there is a cyclical time system which we cannot change very much: the rotation of the planet. However, once you free yourself from such constraints, doors open.
The most likely answer in many science fiction books is that you will assume the time system of the planet of origin for the species that builds the ring. Most likely the species will have evolved some level of interconnection with the natural cycles of their planet and maintaining that cycle will be beneficial for health and well being. It is unlikely, however, that they would include timezones, which would require a prime meridian. If you really get down to brass tacks, timezones are pesky things, holdouts from the railroad era forming a compromise between wanting "12 noon" to mean the sun is overhead and the desire to easily be able to tell when the trains were going to arrive. Without all that pesky planetary rotation mumbo jumbo to get in your way, there's little to no advantage to having timezones. It would be the equivalent of everybody operating on UTC time.
Speaking of which, they might not want a cyclical time system at all. There's a lot of advantages to them, but there's also lots of limitations. For highly technical work, it's common to measure time in seconds since some epoch. For example, most of our high precision timing is built around an "epoch" at 1 January 1977 00:00:32.184, also known as Julian Date 2443144.5003725. TAI, UTC, and several ungodly other ones like TCB all were synchronized at that moment and we've worked from there ever since (the absurd fraction of a minute bit was done to preserve continuity with Ephemeris time... metrology of time is fascinating but ugly at times)
All of our modern computers use this approach as well. Computers don't need a cyclical time system, so they just count straight.
So this should point you to your first hint as to what your dyson ring might use. How important are computers to keeping the civilization running? The more important they are, the more likely they will use computer friendly free-running time, rather than some complicated cyclical system. The more important the originating species is, the more likely you will see carryovers from their home planet.