No. HSAs are individually-owned.
However, if your spouse (and/or dependents) are covered under your HDHP, then you have a higher annual contribution limit. Families can fund up to $7,000 (2019) and $7,100 (2020) vs. individuals who can fund up to $3,500 (2019) and $3,550 (2020). You may also spend your HSA funds on any eligible dependent that's listed on your tax return without tax penalty.
Unique exceptions may apply so always consult your tax advisor to determine which dependent(s) are eligible.
Source: IRC Sec. 223(b)(5)(A)