With neither checked, the form is assigned to taxpayer+spouse. (ProSeries 2019 did this the way you would expect...)

Im using Professional, but I see what you mean, both names appear at the top of the form, only the TPs SSN appears....but even if I chose Owned by Spouse, the SSN doesnt change...but if I look at 2019, it works the same way...so Im not sure what to tell you.

I guess the name doesn't really matter...