I am going to presume your time is probably in UTC.
I would look at converting the time to the timezone you need. Then it gives you more options of how you want to deal with the data, also you could customize the report for people in different zones. For some info about timezones I found this stackoverflow post.
Convert datetime value from one timezone to UTC timezone using sql query
Something like this in an group by clause should work. The code below says if the hour is under 8 then it's still yesterday, else it's really today. You would need to replace the getdate() with the correct column. If I Am correct about that the times are in UTC/GMT I would recommend looking at just converting it to the timezone you want.
case when datepart(hh, getdate())<8 then
cast((DATEADD(day, -1, getdate())) as date)
else
cast(getdate() as date)
end