My parents rent their basement. We told the new insurer (they were switching) about it, and they pretty much didn't care. This was about 4 years ago. They cared alot more about the breaker box being up to date, which we had just gotten changed to 200 amps.
Edit: maybe some care more than others, or it's changed. But it was smooth sailing for us. Premium are higher though. Again, having owner occupied rental tenant for home insurance purposes does not seem to be a big issue. We also rent out our basement and insurer knows about it. Premiums are definitely higher but not crazily. Maybe $50-$70 range?