No, only one person can be named the account owner. If both you and your spouse have qualified HDHP coverage, and want to both make pre-tax HSA contributions or take advantage of the catch controbution once you are 55 or older, then you would each need to open an HSA.
If both you and your spouse have family coverage under qualified high-deductible health plans, the maximum total tax-deductible HSA contribution both of you can make (including employer contributions) is the IRS limit for family coverage. This contribution can be divided between you and your spouse however you wish. If you and/or your spouse are eligible to make catch-up contributions, you may each contribute your eligible catch-up contribution to your individual HSA.