Can I claim head of household if my married son and spouse lived with me for 8 months. I'm widowed and over 65

[SweetieJean]

Did either of them have any income in 2019?

[DoninGA]

If they file as Married Filing Jointly, you cannot claim them as dependents.  If either or both of them have gross income of $4,200 or more for 2019 you cannot claim them as dependents.

See this TurboTax support FAQ for Head of Household - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539

What is a qualifying person - https://ttlc.intuit.com/community/family/help/what-is-a-qualifying-person-for-head-of-household/00/2...

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,200 (social security does not count) in 2019
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.