Does a homeowner have to tell the insurance company that they rent out the basement?

Yes you are required under the terms of you insuring contract to notify your insurer of any change in occupancy lasting greater than 30 days.

Should you fail to do so and a claim arises, and the insurance company finds out that you have transformed the property or parts thereof to tenant occupied, The Insurance company can retroactively declare your policy null and void due to concealment of a known risk even if a claim has already been filed and can deny any and all claims whether property claims or injury claims.