As others have noted, artificial light makes it possible for us to separate ourselves from the natural day-night cycle, but there are still limits to how far we go with this. Most people still live by the natural day. When you're outdoors, sunlight still provides a lot more light than artificial lighting over any large area. (You can light up a stadium with artificial lights, but not a town.) People generally find it more convenient to limit most of their outdoor activity to times when there's plenty of natural light so they can easily see where they're going and what they're doing.
But supposing all we had was artificial light ...
There are pros and cons to living and working in shifts.
The obvious advantage is that you can get better utilization of buildings and machines. Many factories today run 24 hours with 3 shifts. 1 machine running 24 hours a day produces just as much as 3 machines running 8 hours a day. (Well, you have to make some allowance for time for maintenance, etc.) So by running 24 hours the factory cuts its capital investment by 2/3 while getting the same output.
The same principle COULD work in retail. If people worked in 3 shifts, restaurants would only need 1/3 as many tables and chairs, roads would only need to accommodate 1/3 as much traffic, and so on.
As you note, it would be a problem for very small businesses. If the owner of a store is the only clerk, and he wants to work a normal 8 hour day, then he's missing 2/3 of potential business. But for bigger stores it's a non-issue. Instead of having 6 clerks who work the same 8 hours every day, you have 2 for each shift.
Yes, to make it work, people would have to be somewhat more flexible. A company might want to have a staff meeting with all the employees, not just those from one particular shift. Or socially, people might want to have a party with others from different shifts. So people would have to be willing to vary their shifts.
If people tend to work the same shift their whole lives, or at least for very long periods, you might find that society becomes segregated by shift. Someone will find that all his business associates are from the same shift, and maybe even all of his friends. You may find that 2/3 of the population are people you never meet. The different shifts might start to drift apart culturally. Eventually each has its own laws and culture. Etc.
Hmm, I have a sudden thought for a romance novel in this setting: There are huge bureaucratic or cultural barriers to changing shifts, so people divide up into separate cultures based on their shift. One day a man and a woman from two different shifts meet as they pass each other during shift change, or because of some special circumstance. They fall in love, and must struggle to get one of them moved to the other's shift so that they can be together. Their friends can't imagine why they would want to associate with one of "those people" from another shift.
BTW Would people necessarily have three 8-hour shifts? Why not 9 hours or 7 hours? If you're not going by the Sun, who says they have to total 24 hours? Would they have to be distinct? Why not stagger them? Like 8 shifts starting 4 hours apart? Etc.