An HSA is owned by one single individual, there is no such thing as a joint or family HSA. You might be covered by a family medical insurance plan, but the HSA itself is solely owned by one person. Report the HSA contributions and withdrawals on the owner's tax return only.
Incidentally, if you are married, and you are covered by a family HDHP, you are allowed to open and contribute to an HSA in your own name even if you are not the holder of the insurance policy. You share the family maximum contribution limit with your spouse but you can divide it any way you like. For example, for 2023, the family contribution limit (assuming both spouses are under age 55) was $7750. If your spouse contributed $5000 through her job, then either you or her could contribute up to an additional $2750 (2023 contributions can be made up to April 15, 2024). Many banks and brokers will open an HSA for you, there is likely to be a small monthly service charge if not supported by an employer. And the tax savings is slightly better for workplace plans since they save income tax and social security and medicare tax. But you can have your own account separate from your spouse if you want to split your finances that way.
Once funded, an HSA can be used to pay the qualifying expenses for self, a spouse, and dependents, so there are no special limits on using the funds whether or not you and your spouse have separate accounts.
