Potentially, your employer should’ve notified you as part of your separation interview. It doesn’t affect the tax position at all.
Now, it is worth knowing that if your wife is covered by a qualifying family HDHP and you have no other disqualifying coverage, then you are considered to be covered by an HDHP and you are allowed to contribute to your own HSA even though the insurance is not in your name. Your overall family contribution limit is still $7200 for 2021. Contributions made by your wife through payroll tax deduction are exempt not only from federal income tax, but also from Social Security and Medicare tax, so you will save about 7% more by making payroll contributions than you would save by making your own contributions to a private HSA. However, it may be an option you wish to consider, since each HSA account belongs to a single owner and you might have financial reasons to keep an account separate from your spouse, and you can’t do a rollover or transfer from your spouse’s account to your account. You can open a private HSA at many different banks and if you shop around, you may find one with lower fees or better customer service. Just to be aware of.
