Guardian

You do not mention how long the child has lived with you.  

IRS interview to help determine who can be claimed:

https://www.irs.gov/help/ita/who-can-i-claim-as-a-dependen

Am I Head of Household?

https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household

https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household

If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.

He has lived with me for the last two years. 

Q.I was given guardianship of my 8 y.o.  cousin, by his mother. He lives with me full time. Can I claim head of household (HoH)? 

A. No. A cousin is not closely related enough to be a qualifying person for  HoH filing status, even if he is your dependent. A "foster child" is a qualifying  dependent for HoH.  So, if the child is your dependent and was placed by a court order or government agency, as a foster child, then he qualifies you for HoH.  The mother letting him stay with you is not enough to be considered a foster child. . 

As far as being your dependent; 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

A cousin does not meet the relationship test, for QC, but a foster child does.  

A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related (a cousin isn't; a foster child is) OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4700 (2023) ($4400 for 2022).
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer

Thank You. IDK what the IRS is talking about because he sure eats like he is a close relative.