What's in a Name? Anonymous Grading of Writing

As a writing teacher, I hope to encourage and witness growth in my students' work.   Tracking student progress helps me see a student's strengths and weaknesses as a writer.  That said, teachers battle bias like anybody else, so maintaining fairness in assessing a student's writing remains a goal of mine.

QUESTION: If the first item we see on an assignment is a student's name, how does that knowledge re-frame the way we read and assess that work?

In AP English Language & Composition environment, I ask my students to write timed, 40-minute essays, handwritten on paper with nothing but their ID number in the corner (see image).  I do this, I tell them, so that I can grade their work on the College Board's 9-point scale in a fair, objective, unbiased way.  Since students type most of their work, I tend not to recognize their handwriting, so I feel mostly confident that I apply the rubric fairly.  After administering several of these writing exercises, I realized that despite inking comments in the margins, I didn't really have a sense for a particular writer's trends because I didn't know who wrote what.  Anonymity stole the intimacy.

My AP English Language & Composition students list their ID numbers only when they write 40-minute timed essays in preparation for the AP exam in May. I annotate and score them, and only see their identities when I enter the grades into the gradebook.

QUESTION: Is it better (A) to know the identity of a student writer, track his progress over time, and all the while risk bias in grading the work or (B) to ensure anonymity but lose the opportunity to help shape a writer's improvement.

On reading assessments, I like to ask free response questions that require a paragraph reply.  Since I give these quizzes through Blackboard's "test" feature and with the help of Apple's Guided Access and Respondus LockDown Browser, I have the opportunity to grade anonymously a single question across all student attempts (see image).  Again, I can focus on the work (the answer to the prompt), but I cannot connect my observations to the development of a particular student writer.

Many LMSs allow a teacher to score work anonymously. Here I am grading a single "short answer" question "with user names hidden" in Blackboard after a quiz on The Devil in the White City by Erik Larson.

QUESTION: How do you other English teachers handle this conundrum?  Do students benefit more from their work being assessed anonymously or from their work being tracked by a knowledgeable and nurturing writing instructor?