HSA Questions regarding deductions: ownership & misc.

Hello Everyone,

Married filing jointly: For 10 months of 2020 I was the primary health insurance holder (Employee & spouse) under a High Deductible Health Plan - and I also had the HSA bank account. Because of COVID, I was unemployed for the last 2 months of 2020, but there was no lapse in health insurance coverage (it only changed to my husband's employer) - and it was still a High Deductible Health Plan. 

That being said, does the HSA bank account have to be in his name since he is now the primary on the health insurance?...in order for the deposits of $7,100 to be tax deductible? Also, If the HSA bank account is in my name but covers both of us since we are married..do I mark it as belongs to "both of us" within TurboTax?

Thanks in advance.