forget about dpi for renders, you’re rendering pixels that might get printed with a certain amount of pixels per Inch on paper. So if you want to end up with 300 pixels per Inch you need to multiply the amount of Inches x 300 that’s the amount of pixels you need to render.
But on screen it really does not matter a bit how much DPI an image is.
The DPI settings in the Render Properties panel in Modo are only there so you don’t have to go into Pshop to calculate the amount of pixels you need if you want to render for print at a certain size at a certain DPI. ( and you’re using Inches and not centimeters )
Try setting the “Resolution Unit” to Inches and the DPI to 300, now change the Frame Width and Height to something like 5 Inches for both. When you switch back the Resolution Units to Pixels you’ll notice it’s changed to 1500 x 1500 pixels.
So, to render an image that will be 5 Inches wide and high when you print it at 300 DPI you need 1500 x 1500 pixels. Now when you print the same image at 150 DPI, it will be 10 Inches…etc. etc.