What is the name of a cognitive bias by which existing facts are tailored to fit a personal hypothesis?
"I think you are referring to confirmation bias" (from wikipedia)


  Confirmation bias, also called myside bias, is the tendency to search
  for, interpret, or prioritize information in a way that confirms one's
  beliefs or hypotheses. It is a type of cognitive bias and a
  systematic error of inductive reasoning. People display this bias when
  they gather or remember information selectively, or when they
  interpret it in a biased way. The effect is stronger for emotionally
  charged issues and for deeply entrenched beliefs. People also tend to
  interpret ambiguous evidence as supporting their existing position.