So -- we get that the answer to question 7a on Form 8965 (claiming exemtion because the household income is below the filing threshold) is Yes. The question is what to do with Part 3 Coverage exemtions claimed on your return for individuals -- put everyone's name, the adults' names or no one's name. As usual, the instructions were too obtuse to understand.
I think you just didn’t read the instructions carefully because it is quite clear what you do. On page 6 of the Form 8965 instructions, the second paragraph under the Line 7a instructions states: “If you qualify for this coverage exemption, everyone in your tax household is exempt for the entire year. You don’t need to complete Part III.” (Bolding added.) So if you are eligible to check “yes” on Line 7a of the form you do not need to do Part III at all. Nothing obtuse about that instruction, IMO.