Do you think it is correct to change building names to versions you proposed? There are two companies operating in Latvia: Rimi Baltic and Rimi Latvia. Which one is operating here? If not clear, we could drop "Baltic" and simply name this surrounding commercial area "Rimi".

Generally, the name of the territory is added in the "name" tag of the surrounding land use element; otherwise, if there isn't a name, then the name of the company operating the territory is added. But, no matter what, each case should be evaluated individually. In this case, if it is not clear which company is operating in this territory, I would simply name it "Rimi".

I understand the problem with navigators routing through private access roads. That is something to be concerned about, and it indeed can confuse people. But the problems with how routers are programmed aren't the reason to change actual map data. The map should be as accurate as possible.

OSRM seems the most reliable routing solution. It avoids routing through roads marked with the "access=private" tag. Valhalla and GraphHopper ignore "access=private" values, but all three ignore roads with "access=no". Today another mapper changed access values for roads in Rimi territory. So, after a few weeks, OSRM should start routing accordingly.