You don't. You don't provide a lot of detail for non-Obamacare insurance. You merely indicate that you had insurance, and you would have already indicated as much by clicking the box "I had insurance all year". You don't list your non-Marketplace plan by name- there's no place for that in the Affordable Care Act questions.
The only thing that matters for 3/2016-12/2016 is that you were insured. You will indicate that you had "Obamacare" so you can enter the 1095-A. Your 1095-A shouldn't have figures past 3/2016, so the program already knows that you had insurance another way after that.
After inputting the 1095-A for the Obamacare coverage, you are done with Health Insurance. You may receive a 1095-B form for the BCBS, but unlike a 1095-A, a 1095-B is not entered into your return. The 1095-B form simply verifies that you were indeed insured.
