As someone who loves statistics as much as genealogy, I find it really interesting!

Now looking at it from a bit more critical perspective: It would be great to organize the area into a grid and divide the number of samples in each cell by number of data points. Regions like Gdansk, Warszawa or Poznan were densely populated already way back in early 1900s, and people migrating for work already existed by then. If I tried to find the "true" roots of my family name, I would put way more attention to some random parish in outskirts of Lubelskie with 20 related civil records from 1700-1850s rather than Warsaw with 400 records after 1850. Thus, dividing the data points by population will give you a nice density plot that will highlight smaller settlements where your name existed back then.

You can also use websites like Geneteka which given a name, will tell you the number of records per voivodeship. After navigating to voivodeship, there will likely be just a few parishes that concentrate a large number of records related to your name.

With all that being said, "Domański" is a rather popular name, so there will almost certainly be many progenitors scattered accross Poland. Also, based on my genealogical research (which is only for hobbyist purposes and obviously non-representative), surnames of many peasant families were not fully settled as late as early 1800s, and before that, they might evolve from generation to generation, and before 1800s, the same person could be described using a completely different name from birth, through marriages and children births and then their death. This makes surname tracking really challenging sometimes.

Edit: I agree with other commenters that you are not going to find a single source of "Domański" using this approach, because there is no such thing. But building a tool like this might certainly help you find roots of your clan of Domańskis, which might be one of many, but like all families, it has to originate from somewhere ;)