Can I be considered my own household if I rent basement from parent and am claiming a dependent?

If you are filing for yourself and a dependent, then yes. You should be considered your own household.

Yes, you can qualify for the Head of Household if 

• you are unmarried or considered unmarried (your spouse did not live with your for the last 6 months in 2016), and
• you have a  qualifying child, parent or relative as a dependent, and 
• you actually paid more than half the cost of keeping up a home for the year.  It doesn't really matter where you live.