There is lots of evidence that when names appear on exam papers, there was discrimination on the basis of both sex and ethnicity. This is why where ever possible most universities mark by candidate number.
Often the marker was not deliberately women or minority-ethnic candidates down, but their implicit presumptions about groups in society impacted on the marks given.
This test can't be anonymous, hence it it is still likely to be subjected to biases of examiners.
Similar issues arise in recruitment which is why some employers now separate personal information from the rest of the application form when selecting for interview.