Rivers having the same name before and after lakes are a normal thing in Denmark, especially for modestly-sized natural lakes having only one significant inlet. The country is small, so our major rivers are also small, but this map of
Gudenå (bold blue line) shows what I'm referring to. Several natural lakes near the center of the image. A bit further towards the top is Tange Sø, which is named just like any other lake, but is technically a slack water reservoir for a historical hydroelectric power plant. It would be "nice" to have a continuous route for the river, as it has one clear identity all the way, and is popular for canoing.
Another example is currently a
mess on Google Maps. The marker is near a series of "elongated lakes" (without connection), where the broader part of each ends at a historical watermill. The river name "Mølleåen" is used from the larger lake to the west (Furesø) before and after the lake Lyngby Sø (natural and "enhanced" with a dam) from which Mølleåen is meandering to the north and east. I'm considering if the river should be mapped continuously, at least from Lyngby Sø to the coast, but leave the lakes (wide river segments) as they mark where there is water.