This has been debated a lot on here and some people are really passionate about their beliefs. Of course they have different beliefs or there wouldn't be any debate. Some will give you reasons why it is best to use round roosts. Others will give you reasons why flat roosts are best. Some talk about the health of the chicken's feet. Others talk about the chicken's comfort.
I'm in a third camp. Several years ago I did an experiment. I switched tree limbs, a 2x4 flat, and a 2x4 on edge around to see what they prefer. Another forum member recently did a much more detailed experiment with a lot of different material, shapes, and sizes but I can't find the link to that thread. He did find a few things that made a difference. But his general conclusion was pretty much the same as mine. Unless you go to extremes people care about this a lot more than the chickens do. Location in the coop (with mine the preferred location is near a window) is more important than the type of roost. Your 2" diameter wooden rod is larger than the 1-1/2" width of a 2x4, it is plenty big enough.
Marina, believe whomever you wish. I think they'll be fine on your round pole, or you can use a 2x4 flat or on edge. If you decide to switch to a 2x4 or other sawn board, I suggest sanding off the corners. That's not for their comfort as they grip it but more to remove splinters.