How do i run a background check on me if i have the same name as my father?

You tried to use a 'free' website and got what you paid for. If you use a REAL background check company, you won't have that problem.

Note: The paid option from the same website you uses IS NOT a real background check.

A real criminal and/or credit check uses your name and social security number and often date of birth as well. 

Did you put in Jr? OR do it by SSN?

You "run" by name AND date of birth.

You weren't BORN on the same date or in the same place, were you?

Sure, just add a "Junior" to your name.

Try your Social Security Number, or birth date.