What cognitive bias is it when an (ideally objective) evaluation is influenced by the prior opinion of another person?
It's an example of the confirmation bias:


  Confirmation bias (...) is the tendency to search for, interpret, favor, and recall information in a way that confirms one's beliefs or hypotheses.


Research has shown that people have a strong tendency to engage in a positive test strategy when investigating a hypothesis (see e.g., Klayman &amp; Ha, 1978). That is, when testing an expectation (such as in your example) they tend to search for confirming, rather than disconfirming evidence. This tendency then results in the kind of confirmation bias you are describing in your example.

References

Klayman, J., &amp; Ha, Y. (1987). Confirmation, disconfirmation, and information in hypothesis testing. Psychological Review, 94, 211–228. doi:10.1037/0033-295X.94.2.211